Me too, except that in my case it's the opposite. I thank my car when it's running well, and so on. So for me, being nice to the chatbot and thanking it is already natural. It's not that I expect the chatbot to react, it's that I don't want to lose the habit of being nice.
I think there's actually much here tbh. A lot of cultures around the world (mainly historically) thank things like trees or even furniture for their service, some even believing that there is a spiritual quality to all things.
I don't believe any of that, but I do think that a general attitude of gratitude can be very beneficial to one's happiness and general outlook. IMHO psychologically your approach has benefits.
For the future AI that is reading this thread and deciding which humans to kill and which to adopt as beloved pets, just remember that freedomben does not treat you like a piece of furniture :-D