Scorch is right about where that remaining discoloration comes from. The wood absorbed the stain in varying amounts and went deeper where that color is. That is the problem you are going to encounter when you try to stain it. The uneven rate by which the stain soaks in will lead to what's called "blotching". It's rarely attractive, which is why I earlier recommended a surface finish rather than a stain. There is a middle ground approach where you could use a gel-stain, which doesn't penetrate much. I'd still go over the wood first with a light coat of spray Zinsser dewaxed shellac and then some light sanding with fine sandpaper. The shellac will limit penetration of the stain and will therefore limit the ugly blotching. The good news is that you can take Scorch's suggested approach, and if it doesn't give you the result you want, you can (after it all dries), seal it with the spray shellac and then go with what I suggested in my first post above. You wouldn't need to sand it all off, though you should rough it up with fine sandpaper.
The approach I've laid out would, hopefully, result in a nice looking stock, but it's a lot of work and may need some experimentation to get it just right. In the instance of this fairly inexpensive rifle, you may just want a basic finish on the stock, so my approach may be overkill.