Cain’s “disparaging remarks” (the mystery woman’s lawyer’s term) was a reference to when Cain was asked by Greta about the woman’s job performance, and Cain said her work performance was “poor”. That’s all he said. Probably accurate, and no where near as disparaging as the sinister claims against him.
1. to speak of or treat slightingly; depreciate; belittle: Do not disparage good manners.
2. to bring reproach or discredit upon; lower the estimation of: Your behavior will disparage the whole family.
People are way too sensitive when someone speaks the truth. If her work performance was poor, it may have been a disparaging remark, but it may also have been true. (Just as Cain says America needs to get a sense of humor, America also needs to get a thicker skin. If it's true that she was a poor worker, then she brought it on herself by being a poor worker. If he's making it up, then it's slander, not disparaging.)