Background Check

You question does not provide quite enough information to allow for a complete answer to your question. It appears that you pleaded guilty or no contest to the outstanding traffic ticket and paid the outstanding the fines but you do not say whether the failure to appear warrant was recalled and whether you were cited for contempt of court for failure to appear and, if so, the disposition of that charge. You also do not say whether you filed to have your record expunged. Generally, the arrest and any subsequent disposition of the charge will appear on your record and will show up on a background check unless you were able to successfully have it expunged. If it has not been expunged, you should contact a lawyer of your choice near you to discuss the options available to you including whether it can be expunged from your record. Good luck.