と is the quoting particle, でも means "or something" (listing an example just as in お茶でもいかが?
), and the verb is omitted.
In this case it is 思った?
, but in other situations it might be 言うつもり?
or something else.
そんな怒りに妾が怯むとでも?
(Did you think) that I would recoil from that kind of anger or something?
The "or something" can have various effects as it does in English, trivializing the idea, emphasizing it, making it sound far-fetched or ridiculous, etc.
As always, there are various ways to translate this and there is no need to be absolutely literal, but とでも is nothing more or less than the sum of its parts.