What is the procedure to replace carpets in airliners?
The seats are installed on rails, so they can be easily removed (or moved to a different seat pitch). The bolts are in plain sight (random source for example photo). 



The carpets are laid around the rails. I suspect the carpet does not protrude underneath the base board, so they'd only have to remove the seats to get the carpet out. 

This is the inside of an airliner with the seats and carpet removed: