It truly is just that, not letting the opinions of others bother you is the only way. It takes an extreme mental toughness. When I say this I don't mean pretending that you didn't hear, or that it doesn't bother you. It takes a certain confidence in yourself that you can take the negative opinions of others and not let it disturb you because of that confidence you have in yourself as a person, if you know the gossip to be false then there is no reason for you to be offended by it.
Really it all comes down to your ego, the only reason you would take offense to something like gossip is if you feel the need for people to see you in a certain light, you have to lose that completely and just live, you have to truly not care what people think about you. Your actions will speak louder than anything you could possibly say I've learned so just be the person you are and people will see the truth, if they ask about it tell the the truth. If they don't believe you oh well, keep it moving.
It's definitely easier said then done though but that's the only way. You are the only one who can let things affect you.
