When Iris tries to get in Travis' cab, Sport drags her out and throws a crinkled twenty-dollar bill to Travis. Apparently, this is meant to make sure Travis doesn't report the fact that Sport is forcing Iris to remain a child prostitute. Travis keeps the twenty and gives it to the brothel timekeeper after he visits Iris and tries to convince her to leave and go back to her parents.
It seems like the crinkled twenty symbolizes a particularly repulsive strain of corruption and evil. Sport is pimping a twelve-year-old girl, an unambiguously evil act, and for what? Money, of course.
That's what the crinkled twenty is—the root of all evil. Travis keeps it and gives it back to the timekeeper because he's rejecting it. Even though he embraces violence and his own form of nihilistic evil—the kind that leads him to almost assassinate Charles Palantine—Travis hates the corruption and exploitation that Sport represents.
Travis is violent because he's going crazy; Sport is violent because he's morally bankrupt… and sane. Sport's a symptom of the city's own insanity, its money-based depravity, which enrages and repulses Travis—especially when it's used to exploit an innocent kid, like Iris.