I guess the short answer is that no one here knows - LOL
What we do know is it is WWII German, stamped WaA 497, BRG, which was made by H. W. Schmidt in Döbeln Germany. I don't recall ever seeing a brg marked flat buttplate, so I would suggest this was made between 1941 and 1945.
This obviously isn't a common piece. Consider taking pics of the sides and the back so we get the whole picture. The inside should have primer painted on it with an ink stamp. Seeing as how there is pitting on the butt plate, my guess would be it has been cleaned and likely the inside has been cleaned as well.
Best to post on another forum such as the k98 forum where all the German militaria experts are to get a definitive answer.