"I am surprised you would insist upon such a thing. It seems below you." The observation is icy, but it gives her the advantage she needs to press on. A small concession for greater gain; it will be worth it to humble him.
"Very well." She flicks her hair back and composes herself, adopting an expression of honest contrition. "I apologize, Captain Kaufman. I have been short-tempered, shrewish, unpleasant, and slanderous in the course of conversing with you. I have made grossly inaccurate aspersions upon your honor, and offered you a great deal of insult, for which I can offer no explanation save some inborn fault in my nature and may only plead for your understanding and forgiveness in this matter." She bows her head like a penitent, the very picture of regret.
Perhaps she has seen the error of her hateful ways? She even softens her voice before continuing.
"I ask for your indulgence in this, and...it has been a trying journey for me. I should have exersized more restraint of my wilful tongue, regardless, and I no longer wish to quarrel with you."
Or perhaps, and far more likely, she's just being underhanded and trying to throw him off of his guard. There will be time enough to make him pay for forcing her to behave in this way; she already has several ideas about how she'll go about extracting her satisfaction.