The rifle is as noted a 1903 Springfield and dates to around 1921.
At some point it was sporterized and the original barrel was replaced with a Remington 1903A3 barrel. This was done by either civilian owners or by outfits like Golden State Arms and others.
A note here on Golden State Arms. This was a California based company in the 60's that took US GI surplus receivers, barrels and parts and produced sporterized rifles. Golden State stamped the barrels with their name, cal. and model, in the case of the 1903, "Sharpshooter 0f 1942". These rifles were often found to be a mix of 03 receivers and A3 barrels as 03 barrels were somewhat scarce at that point. ALL parts used by Golden State Arms were US GI and the receivers were original Remington as stamped.
During those years, there were a number of players in the game and they all knew each other and were frequently in bed together. However, Nat. Ord and Santa Fe were the only one's that made and used cast reveivers and the serial numbers were stamped in the 5 mil range, the receivers were stamped Nat. Ord or Santa Fee. The bottom line here is what the receiver bridge is stamped as is what it is.
There should be a date stamped on the top of the barrel just behind the rear sight. This will be a 43 or 44 date, ie 4-43 etc.
The bolt appears to be an original 03 with the smooth profile but has been modified, polished, and bent down for scope use.
With the limited pictures, that's about all I can tell you. It has no collector value and falls in that $200 to $250 range.