As you have stated Guantanamo Bay is a stain on our reputation. A majority of those remaining are known to be innocent. Try those who are not, without the use illegally obtained confessions. For those who are innocent repatriate where possible, otherwise strike deals with countries willing to take them in. Pay some form of reparation to the wrongfully abducted.
Though the lives damaged by this will never be fully repaired, it will end a grieve injustice. Despite the damage done to the American reputation, it will slowly recovered if abuses like these truly become a thing of the past.