I wipe the chair down before I use it - they're not doing that. When done, if it looks ok, I just put it back. Otherwise, I wipe it down again and put it back.
And just so you realize - they didn't wipe it after the last dozen kids were in it, so you should definitely wipe it down BEFORE you put your kid in it.
Often I take DD (8 months) out to a fast casual place in the afternoon when we're out walking around. Think a places like Nandos, where you order at the front, and they either call your number or hand you a number and bring it to you. In other words, not typical table service.
I'll then get a high chair from a corner and place DD in it next to our table. When we're done eating, should I return the high chair to its original stack?
On the one hand, that makes it easier for them. On the other hand, maybe they want to wipe it down first?
I always return my tray and dispose of my trash if the place has a place for that (some don't), but it's the high chair return I'm not sure about.