*blinks* I never thought about that conversation meaning that Col. Brandon was rude, or intrusive.

I assumed that he knew Marianne's opinions because she stated them openly. In that case, it would be no more rude than anyone remembering a public opinion expressed in front of them.

Mrs. Jennings's questions and guesses are impertinent because Col. Brandon has made it clear that he wants it believed (or pretended to be believed) that the letter was a business letter. Even should he want to satisfy the curiosity of a woman who gossips so much (thinking she would keep his own secret, if she can not keep her own?), he would not tell her in front of the people he originally avoided telling.