Although you didn't ask, in my opinion, you should sand off all of the old finish and remove the fish belly from the bottom of the stock.
Then, when your raising the grain to "whisker the wood", which is very necessary with walnut, look at the wood in a bright area while it is still wet. You might be more than a little surprised at what you see.
The walnut on these GPR's is often very well patterned and has some great colors. The maker is into mass production and doesn't really give a hoot about the nice walnut their stocks have so, they just paint on a stained varnish to get it out the door.
Give it a shot. Besides a little time, what do you have to lose?
Oh, by the way, ALL walnut is an "open grain wood". It all has exposed grain pores. Some people like them left open. Others like them filled.
You can buy a walnut grain filler made by Birchwood Casey or you can apply the first coat of finishing oil by using 220 grit sandpaper. The sandpaper will remove a little wood and the dust will mix with the finishing oil and fill the open grain, leaving a smooth finish.