The Phillies optioned Llovera to their alternate training site ahead of Monday's series finale with the Mets.
Philadelphia called up reliever Connor Brogdon to join the bullpen as a replacement for Llovera, who was lit up in his big-league debut in Sunday's 14-1 loss. He needed 41 pitches to complete the seventh inning, giving up four runs on five hits and a walk along the way.