The original Jewish custom is to give “Chanukah gelt” (money) rather than presents. There are a number of reasons given for this practice:
We read in the Talmud that the Chanukah lights are sacred and may not be used for any other purpose. The example given there is that one may not count money by the candlelight. Giving out Chanukah money—and not counting it near the menorah—is a way to remember and exercise this rule.
When discussing what a poor man is to do if he does not have enough money to purchase both Chanukah candles and kiddush wine, the Talmud states that Chanukah lights take precedence because they serve to publicize the miracle. The widespread custom of giving Chanukah gelt enabled the poor to get the money they needed for candles without feeling shame.
The Hebrew word Chanukah shares the same root as chinuch, “education.” The occupying Greek forces were determined to force Hellenism upon the Jewish population, at the expense of the ideals and commandments of the holy Torah. Unfortunately, they were quite successful in their endeavor. After the Greeks were defeated, it was necessary to re-educate the Jews—to reintroduce a large part of the population to Torah values. Appropriately, during Chanukah it is customary to give gelt to children as a reward for Torah study.
There is also a deeper reason for this age-old custom. In his record of the Chanukah events, Maimonides writes: “The Greeks laid their hands upon the possessions of Israel.” The Greeks invaded the possessions of Israel in the same spirit in which they defiled the oil in the Holy Temple. They did not destroy the oil; they defiled it. They did not rob the Jewish people; they attempted to infuse their possessions with Greek ideals, so that they be used for egotistical and ungodly purposes, rather than for holy pursuits. Chanukah gelt celebrates the freedom and mandate to channel material wealth toward spiritual ends.
Now, to get back to your question, it is true that the practice of giving gifts on Chanukah has been popularized largely due to Chanukah’s proximity to the Christian holiday season. As such, to maintain Jewish tradition, many Jewish families make a point to give Chanukah gelt as opposed to other presents. Your wife knows what she’s talking about.
This post originally published to http://www.chabad.org/holidays/chanukah/article_cdo/aid/103084/jewish/Why-the-Chanukah-Gelt.htm