What's there to change one's mind about?
The story he told Brienne in the bath makes no sense. No one in King's Landing noticed the placement of wildfire all around the city and then its removal? It seems hard to believe that it was kept secret for almost two decades. The faked moon landing conpsiracies are more plausible.
It also hard to believe that Jamie never mentioned this to Tywin, in which case Tywin would have been sure to let the entire Seven Kingdoms know about it. Until there's some corroborating evidence from a reliable source, all we have is Jamie's word, and we all know what that's worth.
Moreover, Jamie could have tried to disable the Mad King and spirit him away out of the city. It probably would have failed and both Jamie and the Mad King probably would have ended-up dead. But at least Jamie would have fulfilled his vows as Kingsguard. Instead, Jaime defaulted to his usual position of murdering someone while saving his own ass.
Speaking of ignoring his vows, as Kingsguard, he's supposed to be defending the King, in this case, Robert Baratheon, not attacking Ned Stark or running off to serve as one of his father's generals.
Jaime has never shown any contrition or remorse for pushing Bran out the window. Nor has has he show any contrition or remorse for passing off his 3 children by Cersei as Robert's, thereby sowing the inevitable seeds of a succession crisis that would engulf the realm in bloodshed. Until he does something to acknowledge those mistakes and rectify them, saving Brienne from the bear isn't enough for his good act to wash out all of the bad (to paraphrase Stannis). He's still a rotten onion.
Jaime has displayed a lot of self-pity, but then, the unofficial motto of House Lannister really should be "Poor Me", not "A Lannister Always Pays His Debts"
Note: TWoP refugee here. Since I'm discussing matters that have already aired, it's my understanding I don't need to use spoiler tags
