The problem is, if they're doing it right, they won't even know you failed background because of your credit score. Companies outsource background checking to protect themselves from exactly this. They don't even want the potential liability of knowing why you failed the check. They pass your name and address as parameters to the background check company, and the background check company just returns a boolean value. The offer is always conditional upon passing background, so if you don't, the offer is null and void. You don't get to know why.