I think ohen cepel is referring to the star gauge mark that was applied to some M1903 rifles whose barrels were gauged using an early type of mechanical gauge and proved to have minimal deviation of diameter throughout. Readings were taken every inch, and the data recorded on a card that went with the rifle. A special number was also marked on the top of the barrel under the handguard.
AFAIK, the star gauge practice was stopped prior to WWII for the simple reason that improved barrel making methods meant that almost all barrels were up to star gauge standards. Again AFAIK, no M1903A3 or M1 rifles were ever star gauged, though fakes turn up from time to time.
Even if a star gauged M1903 is genuine, it does not mean that the rifle was used by a service rifle team. Many were sold to civilian NRA members who never fired on any team. Nor, oddly enough, does the star gauge mark mean the barrel is accurate or the gun will shoot well. Years ago, a friend had a star gauge Springfield; it shot around a 6" group at 100 yds - not too bad, but no match winner.