"I want to apologise to you, Dillon, from the bottom of my heart," All Stars owner Tony Amrosio said during an interview with the station. "That's not the type of person that I am, my employees are, or my child."
He offered Arnold a $50 gift card. Arnold told the station he wasn't ready to accept it.
The now-former bartender TJ Ambrosio, 18, also tried to make amends.
"What I did was immature and I acted without thinking about the consequences," he said on social media, according to the Daily News.
"I acted in a way that was rude, childish, and totally inappropriate. Due to my actions, I was terminated, rightly so."
Aside from being fired, TJ Ambrosio is no longer allowed to eat in the restaurant, WPRI-TV reported.
The elder Ambrosio told the station he had to call police after getting threats.
Arnold said he isn't blaming the father.
"It's supposed to be professional at all times, no matter what," he told the station. "I don't wish anything bad against him but it kind of ruined by self-esteem a little."