This stamping (K) has been discussed numerous times and remains unknown. Plenty of info that you can sift through on the forum, below is a start.

https://parkerguns.org/forums/showth...t=Charles+King

https://parkerguns.org/forums/showth...rel+steel+mark

The K stamp is thought to be that of Charles Angus King superintendant of the Parker Brothers Gun Works until 1908.... but there is disagreement on this and I'll just leave it as that. I may well be wrong because Dave has poster a picture on the other thread that shows both stamps on the same barrel flats. His son, Walter King took over the position following his father's tenure. Walter King's mark was WK in an oval.





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New to me Parker
 

I have another question regarding the GHE. It has a small compass about 1/2 in. in diameter imbedded in the top of the stock. If I were to remove it, how should I repair that. It really doesn't bother me that it is there as it is part of the gun's history. Here is a picture of the stock with the small compass as well as a few pictures of the game scenes on the receiver.

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A craftsman, such as Brian Dudley, could remove that and correct the stock I am sure. You would have to get with Brian on what that might cost.

That's a lovely old G Grade. The compass may be an indication of the guns use by a grouse hunter. I know I sure get lost in a hurry in the grouse woods. What a great insight into the gun's history.

If I owned that old GH, I wouldn't think of removing that compass.

As a retired museum curator, please leave that compass intact.

I would definitely leave that compass alone!

From my observations, beginning in the mid 138xxx range we see various tiny letters stamped in various locations on the barrel lug, some in the recess like your K --

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and some on the bottom of the lug near the frame size number.

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While K and W seem to be the most common, letters I've observed include V B K O J C X F W and on some Trojans a number. I see plenty of guns in this serial number range, which extends into Remington guns, that don't exhibit these tiny letters on the lug.

I'm sure they have no relationship to the K and Kf barrel steel markings on the early Titanic/Acme and Vulcan barrels.

I had already decided not to remove the compass. It’s part of the history of the gun.