Can I burn an NFT that was airdropped to me?
Technically yes, by transferring the token to the blockchain’s burn address or to a different
address where it is not accessible anymore (e.g., because of lost keys).
This is also ok from a legal point of view if the airdrop was meant to be for its actual recipient.
But burning might be a legal issue if the sender has a legal claim to claim back the airdrop
(see answer to question “Can the person that airdropped and NFT to me later claim it
back?”). Burning under these circumstances might lead to the recipient being subject to a
claim for damages by the sender.
If there is no claim by the previous owner and you are not causing any damage by, for example, burning a high-value NFT, or if it is a clearly shady airdrop, it is possible to transfer the unwanted NFT to a burn wallet, which acts as a black hole, retaining the NFT. Burn wallets have no holders and cannot be accessed or controlled by anyone.