Removal of all "silver skin" is requisite IMHO...
I am now learning that the fat of venison does NOT help flavor as it does in beef or pork nor do the bones so I am going to trim all fat and de-bone from now on... Brent
I agree that removing the membrane is a good idea.
Otherwise, hanging the deer in a cool place to age has served me well through the years. No need to remove fat. Just trim it off before eating, since you're correct about it contributing nothing to flavor---except a negative flavor.
Antelope fat, on the other hand, is neutral. Eat it if you want, doesn't add to flavor. Doesn't hurt.
Best tip of all: GET IT DRESSED, OPENED UP AND COOLED! Hanging in the night air at night in camp is good. If days are warm and you aren't leaving right away, wrap it up to keep cool, unwrap at night. Old sleeping bag works ok.