Canadian Red Wood Stain.

[BVZ24]

Someone here might say I'm crazy, but for temporary touch ups, on a shooter grade rifle, try mixing a small cup of dye-matched canned shellac. Brush it in with a fine paint brush where damaged.
It's fast drying, doesn't react with the oil, easy to work with, slightly more durable than the linseed oil shell, and easily removed with denatured alcohol when the time comes.
It was the finish of choice for the Russians, if that matters.

Edit: Beware the gloss. Any repair you attempt is going to stick out if the repair finish is more reflective than the original finish. You need to buff out the gloss after it dries.