YES and any damage they do to the floor underneath can be deucted from their secuirty deposit, and if it more then you can sue them in small claims court for the difference
It would be stupid for them to do it, and of course since you didnot authorize it you dont have to pay them for it either.
You could evict them as they did break the lease, UNLESS they have some proof the floor was so bad it needed replacement and you refused to fix it.