Assume by “membrane” you mean the OEM barrier attached just under the door panel? When I installed noise dampener inside my door panels I just carefully peeled back the barrier, installed the dampener, then put the barrier back.
Because you’ll be installing the dampener against the door skin through smaller holes in the inner door panel, it will go easier if you cut the dampener in smaller strips to make it easier to install.
Attached is a pic of mine after I installed 6x8 component speakers.