Backstraps are worth their weight in gold, which is why I go into full surgical mode when I trim them. I don’t want to lose a single ounce of meat. A sharp knife and some care will usually do it, but now that I’ve watched this video, I might be buying an old fish skinner. That’s what Marc Wykoff uses on his backstraps, and as you can see, it peels the silverskin off easily with almost zero loss of delicious meat.
Looks like you can pick up an antique Townsend Fish Skinner for about $10 on eBay. If that saves just one bite of backstrap, consider it an excellent investment.