It does look like a finish and or stain was added to the wood.
You have a few options:
1. Leave it - but in this case I think a restoration may be warranted.
2. I like to use a gel paint remover with a simple kitchen sponge and rubber gloves. Despite what people say, I do not find that it turns the wood 'green' but it will dull the wood. This is a great way to remove shellac, lacquer or paint finish. I have used this method on many restorations projects on wood and on metal. Once removed, the wood will look dull, then apply an oil/finish of your choice. There are many threads on what product should be applied within this forum. Everything from Tung Oil, Linseed Oil, Waxes, Howards or a mixture are general favorites. I have used them all with good effect. Realize that anything you do or apply is altering the rifle, it this case it is already altered and 'incorrect', so if you follow the above directions you will at least improve the appearance of stock and you will have a period correct look/feel.
3. If the gel paint remover doesn't work (purely a stain base) then you need to use a liquid paint remover or good old camping fuel (be careful with how you use/dispose of the used rags). This can be applied with good old kitchen sponges or rags, the more times you apply the remover the better result you will have. These products are slow to work and will take many applications, whereas the gel mentioned in #2 works almost instantly. Once you are finished removing the stained finish, you can choose to leave the stock 'raw' or apply a finish as discussed in option #2.
In either method #2 or #3 be careful around any remaining stock cartouches/numbers. If you saturate the wood, it can swell and markings can rise. However, a careful restoration project can often reveal nice and historical markings.
Try to avoid steel wool - in stubborn areas on #2 you could use #0000 wool very conservatively - especially as the stock is already sanded.
Good luck.