You were fired for not understanding the background check form and making a 'mistake' that is functionally indistinguishable from a commonly-attempted lie. Based on the title, you appear not to understand this. Anyone attempting to hire you who gets this kind of convoluted "because I didn't have a degree - well, yea, they have employees without degrees, I mean it's because I said I have a degree, and I almost do, but that was an accident, it was just checking a box on the form" story would probably be very skeptical - you would get further by saying straight up that you made a mistake on the background check form and they have a zero tolerance policy for this. Your current story makes you sound foolish.