What does it mean to " deal with a few raised eyebrows " ?

Answer 1

You do something... people react to what you do.
Some will say nothing (to your face), but secretly question your motives and the appropriateness of your actions. These are the people with the raised eyebrows. (When we ask a question we raise our eyebrows to create a questioning look).

Hence, whether the eyebrows are obvious to you or hidden, dealing with a few raised eyebrows refers to dealing with those who question your actions.

Answer 2

To put up with the judgement of others. Their possible shock.