Grilli retired three of the four batters he faced in Tuesday's 12-2 win over the Astros, working around a double to turn in a scoreless ninth inning.

Grilli pitched the seventh inning in Tuesday's 5-4 loss to the Mets, surrendering one run on one hit and one walk and striking out two.

Grilli recorded just one out during his relief appearance in Wednesday's 22-10 loss to the Marlins and was charged with four runs on two hits and two walks.

Grilli (2-5) took the loss Sunday in Kansas City after allowing the winning run on two hits and one walk with one strikeout in two-thirds of an inning.

Grilli tossed a perfect inning in his team debut during Monday's 7-5 loss to the Red Sox in 11 innings. He struck out two batters and induced a flyout.

Grilli was traded Sunday to the Rangers along with cash considerations in exchange for minor-league outfielder Eduard Pinto, Stefan Stevenson of the Fort Worth Star-Telegram reports.

Grilli was designated for assignment by the Blue Jays on Tuesday.

Grilli recorded two outs while allowing four solo home runs Saturday against the Yankees.

Manager John Gibbons said that he still wants Grilli to take on a high-leverage role out of the bullpen -- a job he was recently demoted from -- but noted that the reliever needs to work out some kinks before that happens, Steve Buffery of the Toronto Sun reports.

Grilli (7.71 ERA and 1.79 WHIP) will be moved into a low-leverage role, and Joe Smith will take over the team's setup duties, the Jays Journal reports.