I assume her problem is that for religious or whatever reasons, she doesn't want to or cannot be alone in a room with a man who isn't a close relative or her husband. Your problem is that you want to have an open conversation that cannot be overheard, so you can both say whatever needs to be said.
In that situation, I think inviting any woman to sit in your meeting, to watch that neither of you does anything inappropriate for a man and a muslim woman, but otherwise not involved professionally with your colleague should be fine. Like invite some software developer to join if your colleague works in accounting or vice versa. So any job related discussions mean nothing to that person who is observing. Obviously ask her what kind of person would be the most appropriate one, because she knows better than you or I.
And that person would be present solely to protect her virtue and reputation. They have nothing, nothing whatsoever to do with the discussion that takes place. It's a 1 to 1 with a chaperone present. That's why I'd say someone from some other department, and also not someone from HR.