Difficulty to dispel depends only on level of the last casting

Teleportation circle has a duration of 1 round.¹ That means each time you cast it, it lasts for about 6 seconds and then goes away completely.

A spell's duration is the length of time the spell persists.

The general rules for spell casting say that a spell ceases to exist after its duration has expired. Nowhere does this spell have text that overrides this rule. There is no way for a spell to have an effect outside its duration unless the spell specifically says there is. This spell does not say anything of the sort.

So, there is no way for the spell level of the other castings to have any effect on the permanent circle because those castings have all expired and are no longer having any effect.

You can create a permanent teleportation circle by casting this spell in the same location every day for one year.

Think of it this way, what level is the second to last casting? Obviously it is whatever level you cast it at. Do the previous castings have any bearing on how hard the spell is to dispel then? No, because only one casting is active. The same logic applies to the last casting except that that one happens to become permanent.

Thus, it would only be the last casting of the spell that determines the spell level of the circle because that is the only spell effect active at the time.

Bonus: this is also the simplest solution

Besides being the solution supported by the rules, this is also the easiest out of all the ways to calculate the difficulty to dispel the circle, which is great news for the DM and the players.

Being that it is only one number there is no calculation needed. Also, because it is the last of all the spells cast there are no numbers to remember. Taking the average (as an example of a houserule one might apply in lieu of the official method), would require the tracking, remembering, and calculation of 365 castings of the spell over a year of game time and possibly more than that in real-world time. That is a lot of numbers. Hope you don't lose the paper you wrote them all down on!

tl;dr On top of being the rules-supported solution, this solution also beats all other methods in terms of simplicity.

^{1 - Since all the spells have similar wordings I'm just going to focus on one of them but the same logic applies to all of them.}

It is up to the group

As far as I know there are no rules covering casting with different levels directly so it becomes a matter for the DM to decided. Though I would advise getting group input beforehand.

Upgrading the level of the teleportation circle

I have four possible solutions for this from most to least favorite:

Take the average

Simply put you take the average of all the spell slot used for all the castings and round that. This follows the idea that each casting imbues the ground with energy and the average energy over the period finally settles in.

This method is the best in my eyes as it allows the most flexibility in casting while still making it hard to set up a permanent level 9 spell. Depending on how you round the average determines how strict it is. If you always round up you make it a lot more lenient as opposed to always rounding down (which would mean you would always need to cast it as a level 9 to get to level 9 at the end).

First past the post

Set a requirement for a number of castings at a certain level to set that level. Simply say that if they want to achieve a certain level of spell at least 50% of the castings should be that level or higher. You could also say that the spell level should be cast in a certain pattern to acquire the desired level like saying the first and last week of the month need to be cast at the desired level.

This option works on the principle that repetition drives the point home. so the most repeated option is the correct one. The pattern method mention also make this method feel very ritualistic.

Take the most use

Count the various levels at which the spell is cast and use the one which was used the most.

This methods rewards a crafty group that plans everything out perfectly by allowing them to get away with using a lot more low level spells to get high results to achieve level 9 you can cast it 122 times at level 9, 121 times as level 5, 121 times as level 6 and once at level 7 for instance.

Weakest link

As suggested by BlueMoon93, you can simply apply the lowest level cast in the series. So 364 times at level 9 and once at level 5 results in a level 5 circle.

This option works well if you want to make your players choose between lowering the level of their circle or missing the resource of a high level spell slot to defend against an attack or something similar. This works less well if the creation of the circle is done in downtime.

Require a single level

Simply say it only works if the spell is cast at the same level every time.

Bookkeeping wise this is the easy option. It unfortunately also limits creativity and play options.

Take the highest/last/first

As suggested by Rubiksmoose. This system would say in various ways that only one casting matters. Either the original casting or the last casting or a single higher casting anywhere in the process determines the level of the circle.

This system makes it very easy to make a higher level circle as only a single high level casting is needed so you can have 1 level 9 casting and 364 level 5 castings to make a permanent level 9 circle. I would not use these options as I think I would be cheapening the endeavor of setting up a level 9 permanent spell. It would mean a single high level character could walk in after others have worked on it for 364 days cast the spell once and have had more meaningful impact on the result then the person who did the 364 earlier castings.

Dispelling a permanent circle

The other approach is changing how hard it is to dispel a spell that has been made permanent by repeatedly casting it.

While the RAW of dispel magic say that if dispel magic is successfully cast (high enough level or successful check) the effect immediately ends. This is something which you could change as a DM. I would suggest by doing this as follows:

Casting dispel magic once on a made permanent spell disrupts that spell or 24 hours. So a teleportation circle is not permanently gone but just non functional for 24 hours.

To permanently remove the teleportation circle you have to dispel it successfully for the same number of consecutive days as it was cast to make it permanent. This might also allow for the option of adding more casting days after the spell has become permanent to strengthen the spell.

But again this is all outside RAW and is for your DM to decide/house rule.

What does your group want?

In the end this is important factor for something that will take a lot of in game if not necessarily a lot of table time. So make sure you have discussed this with your group as to what they want and what kind of play they want in this situation. As a DM you can always just go with the house rule that teleportation circles cannot be dispelled.

They cannot be dispelled once permanent

Take the example of True Polymorph. As shown here (Thank you Rubiksmoose) the wording was updated to say lasts until it is dispelled, instead of permanent.

There is no such wording in these spells, so not only do I read this as RAW, but I think this is RAS (Rules as sensible).

I can't imagine the amount of suck you would feel when a level 5 wizard comes along as dispels the portal you have spent all year working on...

As PJRZ suggested in a comment, this becomes more like a magic item once permanent.

A permanent teleportation circle cannot be dispelled

This is because it is not a “spell” that Dispel Magic can affect - it is the permanent effect of a series of spells.

From Teleportation Circle: “... link your location to a permanent teleportation circle of your choice whose sigil sequence you know ...” . A permanent circle is simply a target of the spell, it is not a spell or magical effect in its own right. I see no reason why they can’t be physically destroyed be damaging the substrate they are part of but they cannot be dispelled as they are not, of themselves, magical.

Caveat: Note that none of the answers on this question are the correct answer, as the rules as written are ambiguous and do not address this. Rather, the answers here provide different possible ways to resolve the ambiguity. Some of the answers, mine included, do not break the rules as written, do not require any house rules, and are different ways of interpreting the rules as they are written. While we can argue about which of these types of answers fits the rules best logically, I think that this answer is the one which provides the most fair results out of all the different ways the ambiguity could be resolved by the rules as written.

One answer to the question about "What is the difference, if any, between permanent and until dispelled?" has a comment, by @FooBar, which says:

Dispel Magic says "For each spell of 4th level or higher on the
target, make an ability check using your spellcasting ability." There
are 365 castings of Teleportation Circle on the object. Once you make
365 successful dispel checks, the circle is destroyed. This will
probably take less than 365 dispel castings, but more than just 1.

I have encouraged that user to turn their comment into an answer.

I think this is a great way to view the permanent circle. It's not that "the last casting becomes permanent", which did not make sense to me anyway. It's not that the first is permanent, or any other single casting. They all become permanent together, as they are all working together. This seems more logical and would fit the description better.

By the time you get to the very last day and make the final casting, there must still be something left of all the previous castings. Some magical energy, spell residue, maybe just the universe remembering what you've done, but something. Otherwise, on that last day the last casting would behave just as the first, and indeed the spell would "think" that it was the first. Each and every casting, down to the 365th, would be "thinking" (for lack of a better way to put it) "Yay! I'm a new circle! And I'm the first one. I hope my caster makes 364 more of me so I become permanent."

Indeed, if I may borrow from my computer background for a moment, if I were to write a computer simulation of a D&D world and included this effect in the simulation, I would have to keep the previous 364 spells around in some way, shape, or form. If I did not have anything at all to keep them around or remember them, then there would be a bug in the simulation and the last casting (and all others) would think that it was the first and no permanent circle would be created.

So if something persists, what is it exactly? Unfortunately for my answer, it is not the full spell effect as you might think of it. It cannot be the full spell effect still hanging around at full power, or the previous circle would still be usable. So it must be some secondary effect of the spell which has a separate duration which is a custom, special duration.

"Wait, but the rules don't say it is a secondary effect with a separate duration!" Yes, that is true because the rules are ambiguous here, so we have to resolve it somehow. And this seems one reasonable way to view the effect.

So something remains. And that something must be building up more and more power over the year. We cannot just say that each special duration ends when the next one begins and remembers nothing from before, otherwise we are back to a similar problem again, as the spell doesn't "know" how many came before.

You can look at this next part in multiple different ways, but they are all essentially equivalent to each other. Either the secondary special duration of each casting lasts until the final and complete ending (365 day completion, or until it "fizzles" from failure to finish), or equivalently there is 1 effect that just keeps growing and gaining more and more power over time.

Saying it is 1 effect with more and more power is fine, except that it leaves you wondering "If it's more powerful than a spell of that spell slot, then how difficult is it to dispel?" and we're right back to where this whole question originated from, and you just have to house rule an ad-hoc modifier to a dispel check.

But if you look at it the other equivalent way, saying that each effect lasts until the end, then you no longer have to house rule the thing which is definitely stronger, and instead you have a straightforward way to let the rules handle themselves. If each effect is still present separately instead of as 1 overcharged effect, then the rules suggest you do a dispel check against each.

How this affects the game

If you look at it this way, you can easily justify allowing the circle to be dispelled and at the same time make it harder to dispel in a way that conforms to the rest of the raw rules. So it is beneficial from a balance perspective and also from a fairness perspective.

Note that this does not require you to dispel once per day for a year, but rather just 365 (dispel checks, not castings) times whenever. So you could succeed at 10 checks per day for just over a month, or more to do it all in 1 day. Or random people could try once or twice to dispel it every now and then, and it could slowly add up to be totally dispelled in a decade or a century.

Unfortunately, this reading does provide the worst possible book-keeping requirement out of all the answers. You would need to keep track of each and every single casting which went into the circle initially, and then you would also need to keep track separately of each and every successful dispel.

Silver lining: This means it would indeed be beneficial to get a 9th level casting in there every now and then to deter low level dispellers from slowly whittling away at it. They could easily dispel the effects one at a time until they got to the next 9th level one which would slow them down for a while.

I don't think the above silver lining is worth all the book keeping that would be necessary, so I would not go with it exactly as written above, but such deviations I made would be house rules.

Despite the annoying book keeping, this strikes a good, rule-abiding balance between "I should be able to dispel that somehow; you can't just say it's invincible" and "You are going to say the villain can ruin my year of work with 1 dispel?!?!?11one Well ---- you all, I rage-quit your stupid game."

Some side effects of this reading

If it takes the power of 365 concurrent instances of the effect to be permanent, then even if you are correct then dispelling only 1 of them leaves you with 364 concurrent instances of the effect, which makes it equivalent to where the progress was the day before it was finished. So does it fail anyway?

This then becomes another ambiguity. If you don't want to make house rules for this, you could treat it the same way you treated the original "long-cast" on the 364th day, since the power would be essentially equivalent to that. So the effect would stop working, yes, but you would still have the potential to save it if you recast the spell to complete the 365 instances again before the end of the following day.

Same as before, but what if 10 successful dispel checks were made against it?

Then the answer is likewise similar. It is now equivalent to when you were 355 days in, so you need to start casting once per day again for the next 10 days.

Just like this entire Q&A in general, these side-effect questions result from an ambiguity, so you could rule differently. I think these responses to the side effects are the way to most closely adhere to the rules and introduce no house rules. And it adds interesting flavor and mechanics and still seems more fair and balanced than the entire effect simply failing completely.