Rumors travel fast, but they get tired. Your character outlasts them.

A story about somebody runs on novelty, and novelty burns out fast. People repeat it for a week, lose interest, and afterward it is only carried by whoever wanted to believe it in the first place. What lasts is the accumulated evidence of how you behave, which builds slowly and is much harder to overturn.

Resist the urge to litigate it this week, since arguing keeps a dying story breathing. Keep being who you are in front of the people who see you every day. The version that survives is the one with the most witnesses.