There is absolutely no indication at all that the Thamor did anything but put up peace as their half of the White-Gold Concordat. It wouldn't be contentious if the Empire had gained any sort of concessions out of the Thalmor in return! It just doesn't make any sense to assume, from basically nothing at all, that the treaty is anything other than what we are very consistently told it is. It is even noted that the terms of the treaty are basically the same as the demands the Thalmor made before the war started, and that such a demand would have been just flat-out impossible for the Empire to concede to until the war reached an end.
This is a big driving point behind why the Empire can be seen as a failing institution for people who pick the Stormcloaks; it really has massively dropped the ball by signing a lopsided peace treaty and then allowing monumental dissent to develop through its enforcement to appease the Thalmor. Thanks to this one-sided treaty the Empire has lost Hammerfell and depending on future choices, Skyrim as well. It doesn't track that they got anything out of the Aldmeri Dominion for it, such an idea runs counter to....well, everything.
The tready that ended the 100 years war between England and France involved concesions on both sides. France lost several territories in Normandy, England was forced to pay a tythe to the French thone for over half of the next century. The points of contention within each power, post treaty, was limited solely to what they were forced to give up, and with the exception of the official treaty doccument, there is next to no recorded communication regarding the concessions of the opposing side within either country.
Do we have the actual White-Gold concordant to read? No. As such, we do not know the specific terms of the treaty. Claiming that the Empire was the only one give something up is argueing from the possition that 'Absence of evidence is evidence of absence'. Thats a logical fallacy.
As for why the Thalmor care so much about Talos, its because of a difference in fundimental philosophy. The Altmer, and by extention all Elves, beleive that they are decended from the divine Et'ada who gave up their divinity to create Mundus. As such, they are effectivly neutered gods. Man, on the other hand, is a CREATION of those same Et'ada, more specificly Lorkhan, a rather unsavory figure in Elven myth.
The Altmer, and by extention the Thalmor, beleive in Talos as a man. There are still some aiive who actually remember him. What they contend is that a Man can become a god, mostly because they themselves are unable of acheiving the same apothesis. If a former god can't become one again, how can a true mortal ever acheive godhood?
THAT is why they dispute the beleif in Talos's divinity.
Of course, Talos was a Dragonborn, and thus carried the divine spark of Akatosh. As such, Talos was less a man elevated to godhood and more an avatar of a god who himself acheived a possition within the pantheon. The Oblivion crisis isn't the proof of that, since the whole end-game was Akatosh's doing and not Talos's, but we know that there has been at least one Avatar of Talos. Avatars require divinity, and thus Talos's divinity has been proven. Alas, the only person who saw was the Nerevarine, and he's off on his little adventure in the orient.