Does it have some special purpose (as you call it a membrane) or it is just to cover what is below? Mine is no more at its place.
I think the leakage comes from the rear wiper motor assembly, and more precisely from its seal to the door body. Originally I had a non working motor full of dirt, so the shaft, turning the wiper, is also an option. Third could be the rear window seal, as mine looks really burned out.
A hint would be the same seal located over the L.H. rear window, where you have some rust bubbling