This is hard to answer without knowing the source text. "Pontius Plate" most likely refers to Pontius Pilate, who was the Roman official who authorized the crucifixion of Jesus Christ, according to Christian scripture. Therefore the white gloves may be a symbol of betrayal or ill-intent. To "wash one's hands" of someone (or something) means to be finished with it; just like you might wash your hands after handling something dirty. It sounds like the narrator is saying that the woman is finished with the narrator and the narrator's companions and telling them by using white gloves as a symbol.