The people inviting and interviewing people at the airlines know what they're doing when they look over an application. When they see a black mark, they're taking it in the context of the rest of what they see on the app. Mostly they recognize that everyone makes mistakes of varying degrees over the course of a flying career.

As has been said, you've had a decade of military flying between your FAA warning and now. Your demonstrated competence in your military career is going to more than offset a single aviation-related oops.