It depends on what kind of 'background check' is being performed. There are a wide variety of companies that sell 'background checks'. Oregon has a state-wide computer system known as OJIN. A very simple search will quickly list all of your state-wide court matters. This includes everything from civil matters to criminal matters and includes traffic tickets and 'violations'.
You may want to talk to an attorney about your options -- whether you can withdraw your plea, or about how you go about cleaning up your record, also known as an expunction.