Official Weber Website
The first step is to remove the sinewy layer on the surface called silver skin.
Slip the tip of a sharp, thin knife under one end of the silver skin.
Grab the loosened end with your fingertips. Then slide the knife away from you just underneath the silver skin.
Continue cutting away from you, with the knife blade angled slightly upwards.
The “cleaned” tenderloins should have hardly any visible silver skin or surface fat.
For great flavor, make a paste of oil, garlic, herbs, lemon zest, and spices. Press it into the meat before grilling.