Often, parents will tell me that they can't take away some of their teen's favorite things because they were gifts from other people. For example, a parent might say, "I can't take away his iPod privileges because that was a gift from his grandmother."
I think you can take it away as a consequence, even if it was a gift from someone else. If it will be an effective consequence, I think it's fair game to take it away for misbehavior.
I wouldn't advise taking away "Christmas" or grounding your teen from opening gifts from other people. But, if your teen is misbehaving, it's OK to remove privileges, even if you aren't the one who paid for them.
Here are some more tips on how to make grounding effective for teens.