Originally Posted by PhysDoc
did anyone take a good look at the 3rd picture?
It looks like the stock was originally made for a different action with the receiver sight a bit forward of the current one.

Pic#4 if you enlarge it (click on the pic) gives a pretty good look at it.
What I would say is a horn inlay in the wood that outlines the existing recv'r sight w/ about an even 1/8" perhaps extra outside of the actual sight .
It makes a nice arc coming off the straight vertical front side of the inlay to then form another short portion which shadows the elevation bar of the sight.
The rear edge is most all hidden by the bolt handle and shadow. But my guess is that it matches in shape to what you can see.

I think it's purpose done extra detail inlay. Not something done to cover a mistake or opening left from a secondary use of the stock.
If the rear sight is not perfectly centered on the horn inlay, perhaps the rear sight was not the one on the rifle when the inlay was done when making the stock.

Horn matrl matches the forend tip nicely and doesn't jump out at you like a 1970's style long aspect white diamond inlay on the side of the stock.
Maybe the orig grip cap to the rifle was that matrl as well. The ivory grip cap was an added feature of a secondary owner wanting to add his/her own 'name' to it with an initial inlay,,again just thinking out loud on the key board.