Travis likes to wear his Marine jacket everywhere—to the personnel office where he gets hired as a taxi driver at the beginning of the movie, to the Charles Palantine rallies where he fantasizes about killing the presidential candidate, and during the murder rampage at the end (among other places). On this jacket, he has a patch on the shoulder, identifying him as a member of "King Kong Company." This was apparently his unit when he was a marine in Vietnam.

According to Martin Scorsese, the King Kong Patch is meant to symbolize the fact that Travis Bickle is like King Kong trying to save Fay Wray in King Kong. Like King Kong, he doesn't really understand what he's doing—King Kong is the one threatening Fay Wray to begin with (although he doesn't realize it), and Travis is doing the same thing to Betsy. He thinks she's a lonely person he wants to connect with, but he goes about interacting with her in a totally crazy way.

In the end, when he liberates Iris from her position as a child prostitute, he plays a still crazy but arguably more valorous role. Yeah, Iris certainly is better off in Pittsburgh with her parents than being essentially an underage sex slave. It's just that there was probably a more rational way of facilitating this than, say, a murder rampage. Like Kong, Travis' aggressive state of being prevents him from approaching things in a less lethal, more constructive frame of mind.