Probably the same way I handle it in places like this....laugh and shrug.
I cannot understand how West made it as far as he did in the military if he clutches his pearls and goes into freak out mode over words. Seriously....I thought we officers were made of sterner stuff.
What you are suggesting he do is what the left wants those they accuse on the right to do. Just take it, move on.,
and be stigmatized for it.
He could not say "stay out of my district" or "stop lying about me on the floor of the house;" indeed, either of those would've been in a manner crying.
Instead he did just what I suspect you would've done in his case, strike back as deliberately as is reasonable, and in deuces, never mind that some would find his retaliation ungentlemanly. She had already shown herself to not be a lady or professional, and also that she was deliberately focusing her attention on him. He had three separate instances of her violating his space professionally and collegially. Enough's enough already.
I think his reaction was measured, appropriate, and called for.