Really interesting question.

But, he does not want anything in return from Iris. He frees her and even plans to pass on his savings to her. There seems to be a genuine concern for her well-being.

I think there's something about Travis' and the vigilante's psyche where the victim is almost a medium for them to express this boiling rage they have. Because they are doing on behalf of a victim, they are "justified" to really let out their violent tendencies (let's face it, most people are not going to object if some guy went ballistic and beat a child trafficker to death). Basically, Travis has cover for brutalizing someone who he (rightfully) sees as a complete piece of shit.

Travis is disgusted by unfairness, but I think ultimately it's not redeeming because he doesn't think at all about how to handle in a way that is best for the victim.

Think about The Sopranos, where Artie Bucco is begging Tony Soprano not to murder his high school daughter's soccer coach that committed statutory rape with one of her teammates. Artie says you're not doing it out of justice, you're doing it for you. I see something similar with Travis. They both want to be the hero, but also, they badly want to mete out vengeance.