In this case, I'd be interested in finding out if the school and/or teacher received a note as well. All of the children came home with huge holiday bags stamped with Santa Claus and stuffed with Christmas treats (holiday themed coloring books, Christmas candy, small toys, etc). I think we went out of our way to make the gift as seasonal as possible without tying it to any particular religion. The Christmas tree has pagan origins, a snowflake is not specific to any religion, and the colors chosen were seasonal for winter as well. It's not like we handed out tiny creches.
ETA: I should also mention that we were solicited for contributions to these bags well before the winter break--so I did not see anything wrong in providing an additional small gift from DD. And I did make sure she gifted everyone so that no one would feel left out.
In this case, it seems like the school itself was perfectly happy handing out explicitly Christmas stuff, and even trying to get parents to contribute to that, so the OP had no reason to suspect that DD's gift would offend anyone, since the school was doing the same thing in an even more Christmas-y way. OP, could you talk to the teacher about this? It might help you to get a better feel for what the other parents in general expect, if there was any negative feedback about the school Christmas stuff, etc.. Plus, the teacher could keep an eye on the child with the offended parents, on the off chance s/he retaliates against DD. Who knows, maybe the teacher will say, "Oh them? Yeah, they find something to complain about twice a month. Guess it's your turn."
I don't think I would tell DD about it. I would guess that while picking out the ornament and writing the note you already had discussions about respecting other people's beliefs--"Why can't we do the Santa Claus?"--and I think at her age it probably wouldn't do any good to tell her someone thought you'd failed.