Hi gl-
IMO, if you feel comfortable enough, you should tell your H thank you for the gift. Sending him a thank you note is nice but could be considered impersonal. You want to act AS IF...as if what he does doesn't bother you. I just think that sending him a thank you note would send a message that you don't want to send...if you know what I mean.

I wish you a much happier new year!

<3
Upside