Honesty is the best policy, and as others have said it is best to fess up and take your lumps on this subject. It is by far the better option to report all prior failures even if you are sure they are not PRIA recorded. That way you are on solid ground. Any other path is risky at best, and while I do think a few pilots who have quit or washed out of non-PRIA training and did not report the event, they took an awful risk in so doing. Only you can weigh the decision having heard our advice. I would much rather admit I had an earlier "challenge" than to deny it and see other, far worse consequences.