[geofft]

Q: "Sorry, we can't proceed without this information." If you're a highly-competitive candidate with multiple offers, that's fine, you can ignore this company or convince them to give you an offer anyway—but if you're the sort of person who would be strongly hurt by revealing your old salary, that doesn't help you because you're also probably less competitive, at least on paper. So this very response exacerbates the gap.

Alternatively, Q (aside): "She's pretty abrasive, should we really hire her?" There are studies that this sort of self-confidence is often perceived as a positive attribute in men and a negative attribute in women.