Reagent Chemical was owned(?) by Tom Skeuse, a Parker collector who wanted to build the Parker again. He tried to find a manufacturer who could built it. The Winchester, Olin-Kodensha plant in Japan made the best prototype, so he contracted with them to built the guns.
Remington owned the Parker Brothers name. They gave permission to build the guns but not the use of the name, so the new guns had to be named Parker Reproductions.
Because Winchester made them, the barrels were stamped "Parker Reproduction by Winchester". The grip caps says "Parker by Winchester".