What does the narrator mean when she refers to mr. brympton as “that kind of gentleman”?

When the narrator refer Mr. Brympton as "that kind of gentlemen", she mean that se does not trust Mr.Brympton.
You can find in the excerpt that the author said 'the typhoid has served me well" before the sentence, which mean that she want Mr.Brympton to paid no attention to her

hope this helps

Sorry ,but i would need more information