Because many future tenants may be allergic to certain pets, it is understood you may need to clean the unit once they move out. So, the cleaning is a fee that is non-refundable.
But if they damage the property, you also want to be covered for that.
I have had landlords charge a pet fee for having the animal every month. Depends on landlord in my experience.
If it's to make certain that the pet doesn't do any damage, and if they do, that you have enough money to repair it, then "yes", it should be refundable if no damage is done.
If it's to have the carpets cleaned after the pets are gone, then it should be renamed a pet "fee", and it should not be refundable.