First, I think it’s important to keep a sense of humor. Anyone who is bored enough with their own life so as to be overly interested in yours… well, enough said.
Secondly, consider the source. Do you trust whomever is telling you about the “rumor”? What is their intention in telling you about the false information? Do they genuinely care for you or do they just enjoy furthering gossip?
Third, how far off is the rumor from actual truth? Is it a slightly twisted version or is it something patently false?
To what extent does the rumor hurt you and those close to you? (For instance, is someone spreading pure lies about you, like…You’re a drug addict, porn star or abortion regular? etc

)
Decide whether or not the subject matter is serious enough to address and whether or not you feel comfortable addressing what may or may not be the source.
If it’s something minor but annoying…like, someone supplying a false reason for why you don’t own a home yet or why you weren’t at mass last Sunday, etc…then I wouldn’t even give such pettiness the time of day.
Keep in mind also that the only thing you’re required to do is live your life in a way that pleases God, whether or not you have human approval. Take pride in His esteem and don’t worry too much about the drama surrounding you, it is only noise that steals your peace.
Also, remember that those who cause trouble generally like to see a reaction. When they don’t get one, all the fun is deflated.