Yes, the landlord can charge a non-refundable pet fee and the security deposit. The non-refundable fee does not form part of the security deposit. The landlord can only charge a fee that is reasonable and is a genuine expectation of damages that will occur. This means that the landlord should have a reason behind charging the amount that they are, and the amount must be reasonable. For example, if the landlord allows dogs, then the carpets in common areas will have to be cleaned more often. The non-refundable pet fee may go towards that expense.
Tenants can try to negotiate with the landlord if they do not want to pay the fee, or want to pay a lower amount. For more information, see our Renting with a Pet booklet.