What is the narrative reason for Jaime losing his hand, Theon sympathising with Jeyne and risking his life to save her or Sandor Clegane's therapy in Quiet Isle . Popular notion is that all of these events kickstart the character's redemption arc (sort of ). Grrm was surprised by the positive reviews for these 3 characters and even classified them as villains.
I would say these characters are presented with challenges that call for self-discovery more than being on a path of redemption.
The only one out of the three who has truly - TRULY - taken a step toward self-discovery and atonement (not redemption) is Theon, because he took a true personal risk to save Jeyne, and invested so much personal motivation to specifically saving her (as opposed to leaving her behind like he wanted with Kyra) that he carried her with his brittle, destroyed body. He understands himself as a villain, he actively chooses to act differently, he takes a real risk with a real cost.
Jaime returning to Harrenhal and jumping into the bear pit was dramatic but his whole plan hinged on others standing ready to save him. Same with all other kind acts. They didn't come at true cost. He is simply being less of a villain, while barely understanding himself to be a villain to begin with. He is flirting with change, but it is very low-effort. Very shallow.
The Hound has done zero to atone. Saving Arya at the Twins was good for Arya but hardly selfless. He is left directionless. He is simply resting in suspension. Is he contemplating his own actions? Does he feel guilt over Mycah, or almost raping Sansa, or any of his other past acts, or is he simply exhausted by his life of anger? We'll see.
I don't see true redemption for any of these characters because they are essentially child killers, and you don't come back from that, but there is dignity in true honesty and atonement, and each of these characters has a greater chance of reaching that place than, say, Dany or Tyrion.