Always return a greeting, to do otherwise is very rude.
Just as an aside: You should know a little vort my father O”H used to say over. Do you know why it is that when someone says “Sholom Aleichem” we reverse the order when responding and say “Aleichem Sholom?” it is because Sholom, being one of the Names of the RBSO, confers a level of Shemirah on the person who is makdim B’Sholom to someone. therefore nothing will happen to him between saying The Shem (Sholom) and the word aleichem. The responder however, no longer has that same Shemira, because he was NOT the makdim b’Sholom, so he says the Aleichem first, just chalilah in case something happens to interrupt his finishing saying the full expression, which would otherwise result in his saying Hashem’s Name l’vatalah.