Originally made in 1921.
I am thinking it has the original barrel which was rechambered from the regular 8X57 (8.0 N) to the 8X64 by Brenneke.
I could have began life as a TypeS. The bolt has been cut to clear a low mounted scope and the steel stock tip is not like a factory tip for a TypeM. The TypeS had no steel tip as far as I know.
What is the barrel length? It could have been cut back and the steel cap added at the time of the rework.
It certainly is special in that the bolt shroud has no provision for the standard Mauser bolt safety.
The Greener type safety is commonly called a Brenneke safety on Mausers. I have seen and had Mausers with Greener type safeties but they have all had the standard bolt safety as well. I have never seen a bolt shroud like this one has although it very well may be a Brenneke item.