Smith, the NFL players union executive director, said he was surprised Gruden felt so comfortable airing racist and homophobic views so casually with other NFL professionals.
The video game developer said it plans to replace the former head coach with "a generic likeness" through updates that will be made available soon.
Gruden, who was gay player Carl Nassib's head coach, used anti-gay slurs when referring to another gay athlete.
"We can't allow them to hide behind their white privilege," Trump Jr. tweeted.
Gruden stepped down as coach on Monday after homophobic, racist and misogynistic emails emerged.
The 2019 series of "Hard Knocks" premieres on Tuesday and will feature the Oakland Raiders for the first time.
Neither the Oakland Raiders nor the Detroit Lions seem keen to take part in the HBO series.
The Raiders slumped to 1-7 after losing 34-3 to the San Francisco 49ers on Thursday night.
It's the worst record since six new head coaches went 0-6 in 2001.
The Raiders quarterback threw three interceptions as Oakland lost their season opener to the Rams.