Post a photo. How moldy are they? A few spots or large area?

It's fairly spread on the exterior molding of two separate doors.

Some here between the storm door as well.

"My question is, shouldn't the door be removed to fully remediate?"

No, that is surface mold and most likely happened just as he said. Cleaned properly, possibly primed again and painted you will have no issues.

Ok thanks for the answer. Should I at least remove the trim to try and clean what's behind it? My primary concern is the mildew also being on parts of the door I can't access, and progressing over the years.

Thanks again!

Its all mildew and will wipe off. Take a bit of clorox that comes in spray bottle for cleaning, and it will wipe right off. Are you sure there is any behind the trim? I wouldnt remove the trim, unless it is necessary. Now that the door is installed, and not laying where it can get that on it, it should not spread or come back, unless its hung in an area, that has a ton of moisture.

I would say your good to go, pulling the trim is not needed. I would make sure he cleans it well (Spic-n-Span works), maybe prime if necessary and top coat.

Vinegar kills mildew, Clorox just bleaches it white. so, clean well with vinegar first, then after wiping well with clean water, wipe anything remaining with bleach.