The Rangers optioned Allard to Triple-A Round Rock on Sunday.
The lefty reliever will cede his spot on the active roster to catcher Jonah Heim, who was reinstated from the paternity list ahead of Sunday's game against Atlanta. Allard was largely been limited to low-leverage work out of the bullpen during the first month of the season, making four appearances while giving up five earned runs on seven hits and two walks across seven frames.