Technically they should stay, at least in Oklahoma. I specifically exclude anything to do with home theater, such as my rear speakers that are mounted to the ceiling and outdoor speakers. Technically they could probably try to make a claim for the entire TV, since it is likely bolted to the mount.
At the end of the day, they can just mostly be pissed off, no one is going to walk over a $40 TV mount and as soon as they close they can not come after you for it (at least in Oklahoma).
Also every house I've ever moved into, or my parents have moved into, have had holes all over the walls. Unless they put in the contract that you will repair nail/screw holes, it is their problem.