It doesn't really matter if they know or not.
If your driving offence is such that you are eligible for a visa waiver, then you are eligible for a visa waiver. It really doesn't matter that you mistakenly put in and then withdrew a visa application.
I doubt if they will know - they would (probably) if you had been refused a visa but not if the application were never considered.
If they do know, it's easily explained - you misunderstood the requirement for a visa.