I want to commend Stanley Allen for his review on this site.  He suggests that the closing scenes are imagined by Travis Bickle as he is dying.  They include the gratitude and respect of Iris's parents, and the return of Betsy, who he now gets the better of by rejecting her instead of the other way around.  I didn't see it that way as I watched the film, but I see it that way now.  Those are exactly the scenes Travis would imagine.  That is exactly the kind of hero he would like to be.  Respectable, desired, and the savior of a young girl who will now go back to school and be good.  It's hard to tell which he would get more satisfaction from - being invited to dinner by Iris's parents or being adored by Betsy.  I think he'd pick Iris's parents.  This makes him a true hero, a clean hero.