Is physical damage to a Remote Control (TRC3 or TRC4) covered by the maintenance contract? I have no idea how it was physically damaged by the client.
Systems, cables, remote controllers, monitors etc. are not covered by the maintenance contract, if there has been any physical damage to it.
So I would advise you to order a new one from Cisco. If the remote controller suddenly stops working (remember to check the batteries first :), then you will get a new one from Cisco, if you create an RMA for it.
Hope this helps,