I've got that same or similar rifle. Mine says "Scoremaster" instead of Target master. It was my Dad's rifle when he was a boy. It was given to him I would guess sometime in the 1930's early 1940's.
Nothing had a serial number until much later......probably after Kennedy was shot.
And I believe mine says "Match Master". It is a heavy thing with big Redfield peep sights but that old gal sure shoots! I haven't looked at it in years.