The purpose for Marie Kondo is to alleviate the guilt for getting rid of a thing you liked at one point. If you thank it, you're essentially convincing yourself that it has fulfilled its purpose and so there's no guilt in discarding it.

LLMs don't fit into that. What purpose could thanking it possibly have other than anthropomorphizing it? If you're trying to break your attachment to an LLM, sure, thank it for the time you spent with it so you can let it go. But thanking it for providing an answer is just silly.

Anthropomorphic Fallacy

https://psychology.tips/anthropomorphic-fallacy/