Originally Posted by Tristan
Harvey: "it's so great to finally meet you, Rachel has told me so much about you. She says you've known her for her whole life".
Alfred: "Well, not yet, sir."
(This exchange is immediately followed by the Joker's arrival.)
I think it had less to do with the Joker than Alfred's personal sentiments concerning Harvey.
It's just a hunch, but I feel like after watching both Bruce and Rachel grow up from children to adulthood, Alfred had developed some fatherly attachment to both. Due to that, he might've secretly hoped they would someday be romantically linked, and that their love would inspire Bruce to be a normal, healthy person, free from any remorse or anger that'd chained him down since his parents' death, that'd inevitably resulted in the birth of Batman. Unfortunately, that dream would quickly fade away by the entrance of Harvey Dent. So when Dent attempted to connect with Alfred, for the purpose of, I'm guessing, get a better chance at pursuing Rachel, it would seem that Alfred's limited response was really a gentle snub from the old butler. Likely he was unwilling to reveal more about himself, or of Rachel for Dent to gain an advantage over Bruce.