Parent was kicked out by crew chief Jerry Lane. This is his second ejection this season and the third of his coaching career.
Manager Robin Ventura said that the dispute went back to an incident from Saturday's game, related to a call in the Sox's game against the Texas Rangers.
"Yeah, it was just something from last night," Ventura said. "It's over, and [you] play."
In a run-in during Friday night's game, Ventura was ejected by then-third-base umpire Greg Bigson after a ball trapped under padding was ruled in-play, leading to the Rangers getting an inside-the-park home run.