Tough call Paramount but I would go with keeping the deposit and letting them try to get it back through the courts.
As a next time sort of thing, when you have the tenants first move in have then sign a preoccupancy inspection that clearly states that there are no signs of urine (stain or smell) on any of the carpet. Then when they move out, you go through the post occupancy inspection, note the stains and have them sign that. At the very least then you have acknowlegement of the urine staining.
Obviously there are no gaurantees here but then the effort to get the deposit back is made by the tenant. Worst comes to worst you lose the case and have to give the deposit back. There are no “damages” that the tenant can claim because you kept the deposit over damage that clearly was there. At worst the judge decides it was normal wear and tear and you refund the portion or all of the deposit.