ICYMI ... the well-respected political consultant-turned-commentator was in the middle of a conversation about the Iowa Caucus on "Rob Schmitt Tonight" when the door behind him opened and a man, nearly naked from the waist down, entered.

DM didn't miss a beat, continuing his convo with the other guests, but it left fans -- and people on social media -- very confused ... questions and theories (and yes, more than a few less-than-tasteful jokes) popped up all over X in the aftermath.

In terms of who this underwear photobomber is -- Dick tells TMZ ... the man walking into the shot is actually his wife Eileen McGann's caretaker who lives with the couple.

Unfortunately, we're told Eileen had a stroke about 3 years ago and has been incapacitated ever since, and she needs the kind of care only around-the-clock help can provide ... which is where this man comes in. Dick tells us the caretaker actually lives with them full-time.

As for how this impromptu mix-up even occurred -- Dick says it was a simple mistake on his part. He says their caretaker knew Dick was doing a hit on TV and had asked him to angle the camera away from where he'd be at ... but Dick explains he forgot to do that.