If this is written up my reputation will be smeared. Please advise if you can. What happened is not even close to violating the law of sexual harassment. AND the employer knows or should know about it but doesn't take remedial action. The intent of the harasser doesn't count.
Harassment is viewed from the shoes of the person who saw it, heard it, felt it.
Third parties, like people who overhear conversations in a lunchroom, have every right to file a complaint about what they saw or heard. Every employee should be familiar with and understand the company's anti-harassment policy. It sounds like your company is doing the right thing by investigating. A fair investigation includes letting you tell your side of the story. Based on what you've told us, this seems like an extremely minor incident which should not damage an otherwise good record.