I for one side with Stephanie on this point, and think Mr. and Mrs. Gardiner probably did not think that Elizabeth had really agreed with him to fix Lydia's scrape.

IMO, when she says slyness seems the fashion and I had not imagined such enquiries to be necessary on your side I think she means that given that Darcy, according to her thought only of [Elizabeth] in his efforts, he must have written to her and somehow informed her of his progress (or more probably of his success if only to confort her as quickly as possible). I do not think she imagined it went further than that.