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]
(..) There's no time to argue now. Get up! I won't go! I can't go until this misunderstanding is cleared up. You won't cheat Miss Melly out of the satisfaction of publicly... ...ordering you out of her house. There was nothing wrong. India hates me so. I can't go, Rhett. I couldn't face it. (..)1939 Gone with the Wind