OE


Evinced, repartee. The opinion about her is clearly negative, so her utterances don't deride (ridicule) negative utterances or elude (avoid) them, but rather demonstrate (evince) them. One isn't likely to fear being bested by doggerel (triviality) or— usually—subtlety (if you're bested by subtlety, you're likely not the sort of person who notices), but clever, quick, and witty replies (repartee) are threatening indeed!

I think elude fits better in the first blank.
The common opinion at the court had it that her droll utterances as often as not elude attitudes unbecoming of a lady.
Lets put it this way: her droll utterance was deemed unbecoming by the common opinion in the court. put double negatives in the sentence to not change the meaning will transform the sentence to "her droll utterance was not deemed (elude) not unbecoming attitude by the common opinion in the court" which is essentially what the problem stated.