Tell the truth...not to us here but to yourself.
If your pet peed on the carpet, even if you got it steam cleaned, then accept fault, cash the check and move on.
If your pet did not pee on the carpet, then by all means take your landlord to court for the remaining deposit. Or, if the carpet was clearly quite old anyway, then take your landlord to court anyway because you would only have been responsible for the depreciated value of the carpet.

