The best stuff to use is "four ought" (0000) steel wool. It's the finest grade available, and will remove the gloss without leaving any scratches. I wouldn't recommend using scotchbrite or any coarse steel wool.
If we were talking about removing 'whatever' residue from blued-steel, then yes, I would very much agree to use 4 ought.
Being that these walnut grips have likely been completely refinished with varnish, the use of (0000) can result in just another highly polished surface.
Though it certainly could be recommendable to start w/4 ought, to notice results, then incrementally 'work into' the courser grades of steel wool, if desired.
If one wishes to get rid of that "refinished wood look", I would recommend 'breaking through' the varnish w/(00), and perhaps a follow-up with (000). You might be surprised at just how fine of a finish that 2 ought will produce on wood, all by itself.
After removing varnish layer, the hand-rubbing of the grips (with your then slightly dirty and oily hands) will produce a finish that will look much the same as illustrated in the photo of thorin6's. This technique acts as a stain.
A light application of boiled linseed oil (mixed 60:40 with mineral spirits), can then serve as a nice protective finish.
...Although, apply too many coats, and buff in between, and your kinda back to where you started ...glossy finish. (Keep in mind that BLO is the main ingredient in traditional varnish.)
While there are many grades of ScotchBrite pads made, the most commonly available "green" (grits are color coded) is a little too aggressive for this purpose.