Delta wants you list all failures (personal and professional) on your AirlineApps. I've had clients list DUI, BUI, minor in possession, multiple check ride failures, job terminations, speeding tickets and they have all been hired. It is about how you explain it in the interview that matters the most.
We are all human and make mistakes. Be upfront and honest. It is the first "core value" Delta is looking for in a candidate. If anybody has a question about their AirlineApps or background please send me a PM. Good luck.