If the restraining order involves violence and the court found against you it will show up on your record. If the restraining order is concerning a boundary dispute or non personal injuries then it would not. I do not believe married or unmarried will make much of a distinction in regard to any restraining order.
Like almost everything dealing with the law, the answer is IT DEPENDS. If your TRO is a CLETS restraining order (which it probably is), than it will be recorded in the law enforcement databases statewide and will show up whenever a law enforcement officer runs your name until the order expires. Whether it will show up on a "background check" or not depends on what sort of background check you are talking about. Any background check that involves a search of a law enforcement database will turn up the TRO. But not everyone has access to such a database, and if there were no criminal charges associated with any of the incidents, then it probably will not show up on a standard criminal records background check, because it's technically not a criminal matter. Keep in mind that any violations of the order ARE criminal charges and may show up. If they review all court records in your name, then it will show up. I've never heard of one showing up on a credit report--it's not relevant. If you don't work in a law enforcement/security type field then it was traditionally not likely that an employment background check would come up with a TRO, but the checks have become much more involved and detailed lately. A TRO might come up if they cast their net wide enough. I would try to determine exactly what they will be searching in advance because not all background checks are the same.