Morris, who was called up earlier this week from High-A St. Lucie, was promoted to Double-A Binghamton upon his demotion.
Morris allowed five runs in 2/3 of an inning on Wednesday night in his only appearance with the Mets.
Verrett, who the Mets lost in the Rule 5 draft to the Orioles over the winter, wound up with the Rangers before they designated him for assignment in late-April. After passing through waivers, Verrett was returned to the Mets on May 4.
This season for Triple-A Las Vegas, Verrett has a 3.00 ERA and 1.23 WHIP in 30 innings pitched (four starts, seven relief appearances).