I don't even use a knife or tool to get the edge of the membrane worked loose.
My trick is to use disposable industrial wiper (ie: workhorse, wypall-x, etc.) they are heavier than a paper towel and more durable. I just use the wiper to dry the backside of the rack, then with the wiper between the thumb and index finger-pinch at the edge of the membrane to get a piece pulled loose from the rack. From there you can start peeling the membrane away from the ribs.
After a bit of practice you can do this effortlessly.