Rogers added that Strop was dealing with the matter "until the fourth inning" before having to tell law enforcement that he had to be ready for work.
"I might have to pitch," Strop told police. "I have to go."
The right-hander recorded his third save of the season in a 7-6 victory over the Dodgers at Wrigley Field, striking out one and walking one in a hitless ninth inning.
Rogers noted Strop had to deal with the "aftermath" of the car theft following the game.
After allowing a run in each of his first two outings back in March, Strop started April with five consecutive scoreless appearances. The Cubs closer had allowed a run in his most recent appearance, though he was credited with the win on Sunday following a blown save.
Wednesday may have included an off-the-field issue, but it also offered him the opportunity to bounce back on the mound. He now owns a 3.52 ERA in nine games this season.
Strop, 33, has called Chicago home since the middle of the 2013 season.