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]
(..) Tell her he ran off with some broad. What do you care? - Watch this. - Don't fuck with them. I will bust their fucking balls. Don't give them the satisfaction, the fucks. Come on, fuckos. Let's go for a ride. Keep them up all night. I will see you later. (..)1990 Goodfellas