Ask the tenant if he is real sure he is never getting another pet for the remainder of the lease. He ask permission for the pet and is now asking for the deposit to be returned because the pet is no longer with him. If you inspect the rental and find no pet damage you should return the money. Often here at the forum the landlords go over the necessity of a pet deposit. The tenant made a deposit when he moved in. Is this not enough to cover any damages and repairs from whatever source? Does it really matter if the pet made them or the humans? Most landlords pay for the pet damages from the human deposit and pocket the pet deposit. When they are question closely about the necessity of the pet deposit they will simply reply that they collect it because they can.