The only information about mounting scopes on Renegade barrels I can offer you is.. see if you can find the correct one from Thompson Center. It will do no good to call them as they don't have any. But I have ran across them on some of the auction sites. They attach to the rear sight and the hole right in front of the tang on the barrel. Those are the only ones I know of.

I do have mounting plates around the house for a Renegade. But never used one. The way I understood it is, you mounted the plate which is tapped to accept a base mount to the plate. On top of that goes the rings. Like I said, I have two or three of them I purchased at an estate sale. Never used them. And am only guessing that is how they are used.