If mr. smith takes a case all the way to the supreme court concerning his being unlawfully jailed, he is trying to see that a wrong be righted. the word for "correcting a wrong that was done" is

"Redress" is the word that correctly describes the word for "correcting a wrong that was done". The word redress is very often used in court cases when a wrong is tried to be corrected. I hope that this is the answer that you were looking for and the answer has actually come to your desired help.