The 03 Mark I's were initially made at Remington Arms starting in 1916 where Mr Pedersen worked on the development of his device. The amount of Remingtons that actually were released to the feds is an unknown. Springfield production according to their records says that in 1920, 91,750 Mark I's were made. In 1921, 10,025 Mark I's were made. If you find a Remington Mark I, it's a rare rifle as there appears to be none accepted by the military. There were no Mark I's issued to troops as WWI was over by the time the concept of the Pedersen device was reality. All Mark I's were put in storage. Sometime in the 1930's, all Pedersen devices were destroyed as it was considered having no value. All Mark I's were refitted with the correct standard service sear and cutoff after the destruction of the devices. It's unclear just how many, if any, were ever issued to troops.
I've had a few Mk I's over the years. Most were rifles issues to ROTC units and also used as training rifles. I've had the honor of owning one Remington but it was unfortunately stolen years ago. The 03 has many variations and the Mark I is just one of them. I've got 03's with Marlin 5 groove barrels, 6 groove Remington barrels, National Match rifles including the rare model NB, and a few rare 03 Carbines that were only issued on the Philippine campaign in WWII. The American Rifleman did an article on these carbines many years ago. The history of this fine rifle is worth the research if you have the time but you need to know if you don't look at the arsenal records, you might be getting the wrong info.