] Perhaps Eleanor has asked him to be careful, since she knows very well that Catherine is attracted to her charming brother.

This is an interesting thought. Eleanor certainly knows that Catherine is enamored of Henry. In Ch. 9 after their talk in the Pump Room

"...they parted--on Miss Tilney's side with some knowledge of her new acquaintance's feelings, and on Catherine's, without the smallest consciousness of having explained them."

(Is that not sweet?)

But I took this a bit differently.

"Miss Morland is not used to your odd ways." ... "I shall be most happy to make her better acquainted with them." ... "No doubt..."

I take this to be Eleanor tweaking Henry a bit. No doubt Catherine will become better acquainted with his odd ways, as would anyone who is in company with Henry - his "odd ways" will always come out and this being the case, one has no choice but to become better acquainted with them.