That's a common finger tap drain pop up. Clean if you like, if not buy a new one. Nothing to them but they often get stuck due to gunk. We have the same thing at our house and my wife has shoulder length hair but they come off like if we have a golden retriever. She seems to take care of it once every blue moon with her 99 cent hair removal tool
https://www.homedepot.com/p/HDX-20-in-Hair-Snake-90830/324601746?source=shoppingads&locale=en-US. It get tossed it after removal.
When I have nothing better to do, I take that damn thing outside and spray it off with the hose and dunk it in vinegar for 30 min, brush it off with a tooth brush (use your wife's and make sure you put it back
), hose it off. Use plumber grease or silicon grease in the moving parts. it keeps it functioning properly and little gunk will stick to it making the next cleaning super easy.