The series, an offshoot of the popular singing with celebrities segment on Corden's "The Late Late Show on CBS, airs on Apple Music with new episodes released every Tuesday".
Linkin Park had posted a photo after Bennington filmed his episode with actor Ken Jeong, calling it a "fun day".
"Carpool Karaoke" first started out as a segment of Corden's "The Late Late Show" on CBS, which was bought out by Apple in July past year after it gained a sizable following.
In a preview for an upcoming episode of Carpool Karaoke: The Series, Metallica shines bright like a diamond as the star of the episode, singing Rihanna's "Diamonds" and "Part of Your World" from Disney's The Little Mermaid.
Comedian James Corden hosts both series.
"We will approach it in whichever manner his family or the people that were involved in that episode, however they would like it to be handled".
Stocks Close Modestly Lower After Trump Warns North Korea
A majority of the major sectors have moved lower on the day, although most are showing relatively modest moves to the downside. Declining issues outnumbered advancing ones on the NYSE by a 1.14-to-1 ratio; on Nasdaq , a 1.11-to-1 ratio favored advancers.
"It's completely up to them and that's a conversation we haven't even thought about having right now", Corden said, adding that the singer's untimely death was "a tragedy".
Talinda, Bennington's wife, tweeted out a link to James' comments and thanked both him and Carpool Karaoke for being respectful of her wishes.
Although the media has reported endlessly about Bennington's death, including reactions from friends and family, it would be disrespectful of Corden and his crew to simply go ahead as if nothing happened.
Losing Chester Bennington was a awful shock; seeing him in an episode of Carpool Karaoke would be incredibly bittersweet.
Carpool Karaoke: The Series - a 16-episode standalone show based on Corden's popular Late Late Show segment - is set to premiere on August 8 on Apple Music.
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