Pena was 1-1 with a 6.20 ERA in 17 appearances before tearing the ulnar collateral ligament in his right elbow. Kinney appeared in 13 games with the White Sox, while Lindsay appeared in four. Lindsay became the first Australian-born player to appear for the White Sox.
Cofield and Septimo did not appear in the major leagues this season.
The White Sox’s 40-man roster is now at 36 players.