After having heard two separate backstories (each of which is notably applicable to the person who he tells the story to); we can assume that the Joker's origin stories are lies; intended to both manipulate, distract, and add to the perception of his unhinged persona.
During Joker's third (attempt at a) story, Batman completely ignores the Joker's attempt at starting a conversation, and continues with the fight that is occurring.
If I had to put Batman's reaction into words: Quit your bullshit.
We don't know for sure what the Joker would have said. But given what we know of the other origin stories; the third story would be one that is very applicable to Batman.
E.g. about how the scars are Joker's punishment for being a dictatorial bully (which is a not-so-hidden analogy for suggesting that Batman will at some point be punished for his deeds).