So the real issue is are they calling it a pet, an ESA (emotional Support animal), or a service Animal.
Service animals are trained and cannot be denied. You may ask for paperwork to support their training. It does not give them the right to break any rules like barking, bathroom use, damage, etc.
ESA animals are allowed ONLY with a Dr.'s note. There is no registration service for ESA animals though many will try to convince you there is. Again being an ESA animal does not give it any rights to break any rules.
If it is just a pet I would offer for them to house the animal elsewhere. And for me personally it would depend on the length of the stay, the animal, and why you have a no pet policy to begin with. At a minimum if you let them stay, you should let them know there is a pet cleaning fee and daily pet rent that will be do. Set it so they make the choice you want.