Dismissiveness is a put-down. It wasn't just the comment about Mrs. Clay.

Elizabeth will not give serious regard to anything Anne says, even a serious warning to a hidden agenda that could change the whole course of their lives.

"Anne was so impressed by the degree of their danger, that she could not excuse herself from trying to make it perceptible to her sister. She had little hope of success; but Elizabeth, who in the event of such a reverse would be so much more to be pitied than herself, should never, she thought, have reason to reproach her for giving no warning." (5)

"She spoke, and seemed only to offend. Elizabeth could not conceive how such an absurd suspicion should occur to her; and indignantly answered for each party's perfectly knowing their situation." (5)

It is an example of more dismissiveness with ample verbage:
(The paragraph beginning "Mrs. Clay," said she warmly, "never forgets who she is;"...etc.) to 'prove Anne wrong' (my quotes for my words) as if talking at length provides more truth than Anne's (we presume) simply stated warning. In my opinion, Elizabeth's comment on Mrs. Clay being safe is to shut down the conversation. (It also reveals something more of Elizabeth's confidence of being the sole person of importance in Sir Walter's life.)

Elizabeth has superiority needs and uses Anne here by putting her back in her subordinate place.

"However, at any rate, as I have a great deal more at stake on this point than any body else can have, I think it rather unnecessary in you to be advising me." (5)