He says the mailman was actually a woman and was late, despite this statement being unneeded it makes sense and theres no indication of it being false.
the point of the 'woman' line is, again, we're adding a twist to the end of the line. like the end of the taxes line, or the end of the skipping work line. the idea of a mailman who is a woman seems fun to me because the word 'mailman' sounds like it's a man. but it's actually a woman. and i just thought it was an interesting place to reveal someone's gender.