Just a wild guess and probably way off.
The one on the left looks kinda like a cartridge box, the 15th Corps corp badge. The one on the right looks kinda like an acorn, the 14th Corps corps badge.
Like I said, a wild guess.
Likely done post war. I've run across several corps badges carved or inlet into stocks in the last few years.
Handled a LG&Y Special Model with rock solid provenance to a member of the 1st MN with a corps badge inlet on one side of the stock and a hat badge on the other.
These were govt property and a soldier would be fined and punished for defacing govt property. But once he got it home it was his.