It is mean, but I imagine that Anne feels more "the plague of Mrs. Clay" than she feels the sting of Elizabeth's remark.

I am always bemused by Elizabeth's preference for Mrs Clay, for it really is inconsistent with her attitude about the Lady Dalyrimple and Miss Carteret: "Family connexions were always worth preserving, good company always worth seeking" (ch. 16). Mrs Clay is neither family, nor "good company" (in that, she is a complete nobody, while Anne is the daughter of a Baronet, as well as Elizabeth's sister). It's just another example of many in which Elizabeth and Sir Walter shed their love of rank and consequence where Mrs Clay is concerned. In these cases, the sycophantic placating apparently far outweighs the social degradation they risk, in associating with such a nobody as Mrs Clay.