Wright's initial youth loan arrangement came to an end after Saturday's 2-2 draw at York City, in which the 20-year-old bagged his sixth goal in 28 appearances for the Pilgrims.
Ahead of the player's 21st birthday next week, Wright will now spend the remainder of the campaign with the Pilgrims on a standard loan, which includes Grimsby's option to recall him after the initial 28-day period.