Xbox 360 Mic Problems

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Okay so it's not really a problem with the mic, but a problem with hearing other peoples mic. Sometimes I can't use my mic, because there are people in the room next to me or something and I don't want them listening. The problem is, i still want to play online. If i meet other people online that have mics, then what they say will come through my T.V. Is there a way to mute this? from what I saw, you can only mute it while the mic is plugged in, but then the other person can see I have a mic plugged in, so they get mad when I don't talk to them.