Apart from being annoying, this stuff actually serves an important purpose - it prevents water ingress via the door, and given the fragility of early R3 door cards (literally made from…card), this is not a bad idea.
The membranes usually only survive removal once or twice, tearing and never going back on neatly, not to mention the Butyl tape sticking to just about anything.
So…here’s how to deal with it and create a professional, dealership (or better!) repair.
You’ll need some new Butyl tape and a sheet of membrane, as well as a socket set, plastic trim tools (very important to prevent scratching paint & trim), a heat gun and screwdrivers. I won’t go into the door card removal and window regulator replacement processes here as there’s plenty of tutorials/instructions around should you need.
Unfortunately greeny/yellow Butyl tape as used in the factory isn’t easily available, and it goes off when stored - so I advise any left over to be kept in a sealed, airtight Ziploc bag.
Once you’ve removed the door card and peeled back the membrane (keep it as intact as possible), you’ll be left with a load of probably hard, messy, old Butyl tape.
Your task now is to remove it. Scraping it takes ages, so the best way to make the process as neat as possible is to use a heat gun to warm and soften the tape. Using a trim tool, it should neatly scrape off the door in pliable lumps.

Once you’ve removed it all, use some degreaser such as tar remover to leave a spotless finish.

Then, take your old door membrane and lay it on top of the new one, tracing out the outline, plus any cutouts for the speaker. Cut the new membrane using sharp scissors.
Apply the new Butyl tape around the door in the same location as the old one - there should be a handy track in the door to follow. Press the new membrane into place - it should stick neatly and easily on the new Butyl tape, and look like so.

The screws will easily pierce the membrane, but you’ll need to make holes for trim clips to go through.