If a landlord charges say a 300.oo pet fee, does it have to be refundable or can they keep it?

It is on his terms. Ask him what he says?

It may be either way, I normally had in my leases that I would keep pet fees but could still charge more at their leaving if their pet did more damage than the pet fee and the regular deposit would cover. The pet fee is normally used by me anyway, to try and discourge them from having pets

But it will be what ever the landlord wants it to be, and written into the lease, you then have the option of renting or not renting