Lilly was ejected Monday after he told Davidson to "concentrate" more. However, Davidson, who was the home-plate umpire for the Cubs-Pirates game that night at Wrigley Field, disputed the pitcher's comments.
"He never said that," Davidson told the Chicago Tribune when asked about Lilly's comments. "I just found out I scored just about a 96 [out of 100] on my plate job, so my concentration was pretty [darn] good in my opinion."
Of the 215 pitches on Monday, Davidson told the newspaper he missed 10 as determined by Major League Baseball's grading system.
Davidson said "everything [Lilly] said to [the media] was bull. Everything I read in the paper that he said was untrue. He never said one of those words. What he said to me, you couldn't print in the paper."
Hendry and manager Lou Piniella are hoping to move on.
"Umpires are professionals the same way players are professionals," Piniella said. "Umpires get paid to call a good ballgame, and arguing at times, unfortunately, is part of the game, and it's been that way forever in baseball.
"I don't see where us or any other team gets penalized unduly for something like that. One thing I did tell Ted Lilly is we're going to put barbed wire over here on the fence."
Lilly jumped over the fence in front of the Cubs dugout to continue his argument with Davidson on the field.
"We all know Ted Lilly is a real standup guy," Hendry said. "From an umpire's point of view, I don't think Ted is considered in any way shape or form, a guy who complains. You don't see Ted on the mound complaining about pitches, rolling his eyes, walking around on the mound.
"I would think Ted's reputation with umpires is real good. He's a winning type pitcher and a fierce competitor, and his record stands for itself."
Carrie Muskat is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.