This is a funny topic!
They used to collect the F menus about an hour before landing (often when people are changing back into clothes). I'd stick mine in my bag BEFORE I left my seat or sure enough it would be gone when I returned from the lav.
I am sure they would not refuse if you asked. Or just put it away and you won't need to ask at all.
Most people speak to others "in a respectful tone", so I am puzzled by that comment above. (? odd)
I've never considered taking the leather binder - don't get the point? The menu pulls out of it, that's all you really would "need"!
Air Tahiti Nui does the same thing - you just have to pull the paper menu out of their nice "holder" as well!