The 19-year-old, who arrived at The Jakemans Stadium in the summer from Chesterfield, will now spend the remainder of the campaign in the East Division of the Evo-Stik League with the Owls.
Parkin's only competitive outing to date for the Pilgrims was cut short by a red card in July's Lincolnshire Senior Cup defeat to Lincoln United.
The Pilgrims have retained a 24-hour recall clause within the agreement.