A restraining order is typically a civil proceeeding and not a criminal matter. As such, the record of a civil restraining order application showing up on a background check where no issued order resulted most likely will not appear.As to correlating you with the application with the restraining order where your date of birth is not listed in the application most likely will not pop up as to you later on in a general search. Since the application was a civil matter with no order resulting, you really should not have to worry about any negative outcome as a result.