When I burn an airdropped NFT that I do not want, can I ask to get the gas fees refunded from the person that airdropped me the NFT?
Usually no, as there is no real reason to burn an airdropped NFT. A legal claim that could
cover such costs could be a claim for damages. But if the damage has occurred because of
a voluntary act of the damaged party (here: the one burning the NFT), the law does not allow
for a refund. Usual damage claims are valid for involuntary damages only. However, there
might be specific circumstances where there might be a legal claim for a refund of the gas
fees, e.g., because the airdropped NFT needs to be burned because it infringes the rights.
Burning an NFT is your choice and not something you need to do to prevent any damage. It is possible to simply hide the NFT from your wallet and forget about it. If you decide to burn it and pay the gas fee, you will probably not be able to claim the amount spent.