Or, to more accurately convey the sentiment, "Mary doesn't want Joe Blow
and his brother to be knocking on her door."
But "Tom, Dick and Harry" suggests you're referring to more than just
generic, faceless slugs: Tom, Dick and Harry are distinguishable from
each other, although they seem to have been culled randomly from some mass
pool. Joe Blow, on the other hand, is a faceless slug: you can't tell
Joe Blow from another Joe Blow (or his brother).
If this interpretation is correct, why is the phrase out of vogue?
Tom, Dick and Harry. I dunno. My primer was *Fun with Dick and Jane* and
there is a temptation to suggest these names come from another set of
primers.
On the other hand, Cole Porter wickedly used this in *Kiss Me Kate*
Bianca sings how she wants any Tom, Harry or Dick, and at the end of the
song, trills on "A Dick, A Dick, A Dick.." It's in the movie too. It's
amazing how it got past the censors.