Question about background checks?

Hey y’all. I recently accepted an offer at a company and am now being asked to complete a background check. For one role on my resume, I listed a company that I did “contract” work for (it was a few gigs that I was paid cash for). For a previous employer I listed myself as an independent contractor, and I can’t remember what I put on the background check. I’m just obviously nervous now that I have a companies name tied to the role. I know the background check will pass with my two most recent employers (i did not embellish my title, duties, or employment dates). Should I just omit that third job on the background check since I know there is zero documentation that will connect me to it? Will HR at my new employer cross reference the background check with my resume?