Look at it this way: How would you react to receiving a Ramadan greeting card from a Muslim friend, given that Muslims believe that Islam is the completion of Christianity? Would you not prefer to receive a greeting card wishing you well on a holiday you do celebrate, such as Christmas?
Given that there is no consensus within Judaism about the appropriateness of greeting cards for Hanukkah (some Jews exchange Hanukkah cards; some feel it is an inappropriate adaptation from Christmas) and given that Hanukkah has now passed this year, I suggest sending your colleague a New Year’s greeting card. I cannot recommend sending a Christmas card, particularly one that carries a strong Christian religious theme.
