De is more formal than des. Without context, I’d say that Woman uses formal language, which is not the case for Man. Or Man considers “bas méfaits” as a kind of compound noun, thus conveying the fact that he has trouble understanding what those “méfaits” really are and what Woman means. In this case, des is fine even in formal language.

I believe the presence of si makes de mandatory here. It could be either in the answer though.

Woman: Quelle déception de te voir t’abaisser à de si bas méfaits.

Le bon usage states that when the noun (méfaits) following a plural indefinite article (des) is preceeded by an epithet (bas), the indifinite article is usually replaced by de:

• De bons fruits
• En faisant de plaisantes grimaces (Marcel PAGNOL)

→ This is the rule applied by the Woman in her statement.

According to Le bon usage again, an exception is made when the adjective and noun form a whole together:

• Des bons mots
• Des grands hommes
• Des grandes personnes (= des adultes)

So in the perception of the Man of the question, bas méfaits is likely considered as a collection of individual bas méfaits (and therefore, a “bas méfait” becomes a full concept, different than a simple “méfait”).

In my understanding, by responding:

Man: Des bas méfaits ?

, the Man is basically asking some details and/or examples of the individual “bas méfaits” the Woman is referring to in her accusation.