The charge must be proved 'to the satisfaction' of the court. [=the court must be convinced that the charge is true]
I complained to the manager about the poor service but did not get any 'satisfaction'.
The work was not done 'to my satisfaction'. [=I was not satisfied with the work]
(..) decided he would not stand for this besmirchment of his honor. He claimed the critic didn't understand what it meant to be a man, so he demanded satisfaction in the form of pistols at dawn. He wrote the paper, this letter, saying anyone who didn't like his book, he would challenge to a duel, (..)2018 TvShow: BoJack Horseman Title: Free Churro Season: 5 Episode 6