I want this for the feels. It's normal in human interactions to say something like, "Thanks, that's a good answer," when someone helps you out. I bugs me to just walk away/close the window after asking the AI something (particularly if there was some back and forth discussion). It feels like I'm snubbing someone.
However, I don't want to literally query the AI with a thank you message and waste resources in some data center somewhere.
Provide a simple button, maybe something as simple as, "Thanks!" or a thumbs up. The user clicks it and feels like they've done the necessary, courteous, thing. The app may, or may not, respond with a canned, "you're welcome."