Just be a little careful with "Scotchbrite" pads.
If they will take the Teflon off a new saucepan and cut though blued surfaces like a grinder, they may be a little TOO much for a varnished, but hopefully un-sanded stock.
Depending whether the offending "gloss" is "Two-Pack", Marine or "domestic" varnish, the technique will vary.
Any of the more interesting solvents that break down "varnishes" should be OK for a slow, but thorough removal, without taking crisp edges (if any survive) on the wood in question.
Enthusiastic application of the hot-air paint stripper gun may appear attractive, but it also may cause some very unattractive distortions at the same time. "Warp Factor Nine" belongs on Star Trek, not your prized woodwork.
The "Two Pack" epoxy type finishes are pretty tough. Long exposure to Acetone will probably break it down, but it will still take a lot of careful scraping with a wooden or plastic spatula to get to the timber. About ten hours contact with liquid acetone will cause the outer gel-coat (coloured resin) on fibreglass mouldings to deteriorate badly. (Think: About a litre of acetone spilled in the transom well of a speed boat and left overnight on a cool evening; NOT pretty!)
Then, because the "solvent" will have penetrated into the timber and started to leached the good stuff out of the wood, systematic re-oiling is vital.
But, done properly, to GOOD furniture, the results easily justify the effort.