[Michele]

I'm not so sure the point of producing these special guns without markings just was to prevent the identification of the country producing it. Serial numbers and manufacturer's markings were used by intelligence services to glean intelligence. The factory or factories that produced the gun, a ballpark figure of the numbers produced, and so on. Nothing transcendental, but somewhat useful anyway.
When it came to the Allies, who were the ones carrying out a strategic bombing campaign, these small details might have boiled down to whether or not a certain German town with a certain factory would be unlucky enough to end up on a list of targets.
Guns intended to be dropped in occupied territory are by definition more likely than other guns to end up in the hands of the enemy intelligence.