[He's had worse thrown in his face, unfortunately. Gilgamesh just endures it, staring straight at her, unimpressed. And while he could retaliate in a most violent way, a way that would leave her choking on her own entrails, he leans back instead. Leans on the handle of said mop and just casually reminds her:]

Truly, if you know of me, you know I am not the sort to hold back on account of some obstinate woman.

[Which was his way of telegraphing to her that she was starting a fight she couldn't win. He shakes his finger, scoldingly.]

One last time. Your name. You will provide it, or I will provide a sure and swift beatdown for your insult and disrespect.