A pet fee is generally not refunded, while a pet deposit may be refunded depending on the condition of the rental home at the end of the lease. The landlord and state laws determine if a separate pet fee or deposit is allowed on a rental.
Some landlords use the words "fee" and "deposit" interchangeably, so it is important for the renter to verify whether or not it is a refundable payment. Even if the landlord considers the amount paid refundable, the renter isn't guaranteed the money upon moving out. The landlord may keep part or all of the amount to cover damage or cleaning costs associated with the renter's pet.