Perhaps he tells Caroline about Elizabeth's "fine eyes" simply to make clear to her that her suppositions are wrong. Maybe it really is that simple. :-)

Here's the quotation:

"I can guess the subject of your reverie."
"I should imagine not."

"You are considering how insupportable it would be to pass many evenings in this manner -- in such society; and indeed I am quite of your opinion. I was never more annoyed! The insipidity, and yet the noise -- the nothingness, and yet the self-importance of all these people! What would I give to hear your strictures on them!"

"Your conjecture is totally wrong, I assure you (ch. 6).