That scope looks like a reproduction unit to me.
That means you aren't going to devalue it if you refinish it.
Some folks get all worked up over refinishing or cleaning up put togethers or copy cat rifles.
I like these rifles because they allow me and others to get the fun and experience of owning, handling, learning about and shooting types that I normally wouldn't be able to afford or be willing to add more wear to.
I have fixed similar scratches on those scopes.
They don't add "character" when they're bright and shiny, such as that in your pics.
I take the scope out of the rings first.
Find some good 80 grit Emory cloth.
Grasp one end of the scope firmly in soft pad vise jaws and use the cloth to clean up the scratch until it blends in. Be careful, when you go to blue the scope tube, if any of that scratch is left behind, it will show up. It's up to you to decide how much you will find noticeable.
I remove all of the finish from both tubes with this method, then use a good cold blue as mentioned above.
The relatively coarse Emory cloth will duplicate the rough machining marks if you're careful not to try to use lengthwise strokes.
Just apply the Emory cloth to the tube in the same direction as the machine marks.
Every type of cold blue has its own look, in that some are darker than others or will work better on certain types of steel.
You may want to try whatever type of "cold blue solution" you plan on using on the scratch before removing the finish.
Depending on the steel used for making the tubes, they may or may not have high nickel or chrome content and won't work with your bluing solution.
If push comes to shove, you can use permanent markers, such as those found in pens, such as Sharpies, to carefully cover the scratch. These fixes are only visible on close inspection and if you sell the rifle, full disclosure should be given.
