This q was actually just on Halacha For Today’s newletter. I’ll copy it here:
Reader’s Question:
Where is the makor (source) in minhagim seforim or even Halacha to give gifts on Chanukah?
I strongly believe it is none other than chukas hagoyim one hundred percent.Chanukah gelt perhaps has a source, however, this business of giving gifts? Where does that originate from? I am hoping that perhaps you can change my opinion.
Answer:
The Poskim disucuss this and conclude that it isn’t a problem of Chukas HaGoyim, as in all likelihood the Goyim’s minhag of giving gifts on their holidays was taken from us and not vice verca. (See Emes L’Yaakov from Rav Yaakov Kamenetskky Zatzal Siman 670 in the footnote.)
The Ponovez Rav, Rav Yosef Shlomo Kahaneman Zatzal said that after the greeks forbade the Jewish children from learning Torah, their parents had to “bribe” them with gifts to get them to learn once again. Giving gifts on Chanukah commemorates that aspect of the Chanukah miracle.
Indeed, children should be told when receiving gifts that it is for this reason and that they are expected to increase their Torah learning because of the gifts. (See Sifsei Chaim from Rav Chaim Friedlander Zatzal; Moadim Vol. 2 page 134)
See also Shu”t Avnei Yashfeh Vol. 1 Siman 129:2 and Sha’arei Halacha U’Minhag Vol. 2 page 283