Remington was "issued" the old mothballed machinery from Rock Island Arsenal left over from when RI stopped producing the 1903 Rifle at the end of WWI. By all accounts the machines and fixtures were in a sad state of affairs after sitting neglected for 20+ years. Remington did the best they could as their contract was for rifles intended for Lend-Lease to England, with some production earmarked for U.S. use. (Mind you, Springfield at the time was nose deep in trying to get Garand production up to speed and had no time to devote to building more '03's.) The early Remington guns were ok, not quite up to the high standards of pre-war Springfield stuff, but very good nonetheless. As the old machinery continued to wear out and the need to re-tool became apparent, and the demand for rifles of all types was through the roof, Remington approached the Ordnance Dept. for permission to substitute stamped parts for non-critical milled parts, sight changes, and to take a lot of other time saving shortcuts in production such as attention to finishing. The resulting rifle was enough different from the standard M1903 that it was designated the M1903A3.
Remington '03's are a great addition to a rifleman's battery, IMO.
