Most likely the registrar will transfer the name if you lost. You probably can't even atempt a transfer, since the filing itself would have locked the domain at the registrar dissallowing the respondant to transfer, change DNS, or change whois contacts.
Unless you think the case was decided improperly in the legal sense, a civil suit is probably the only remedy, and an expensive one. Unless you have a lot invested and wish to invest more with the possiblity of losing that too, it's probably best to move on.