Bennington, the group's lead singer was found dead on July 20, and this episode was filmed July 14.
The family of the heavy metal superstar gave their blessing to release the footage onto the band's Facebook page, where it surfaced on Thursday.
On that day, the band shared an image of themselves and Jeong on the set to Twitter, with a caption to say it had been a fun day with Jeong and to "stay tuned".
In August, Corden said that the decision to air the "Carpool Karaoke" episode was up to Bennington's family.
The episode, in which the band and the "Dr. Ken" star drive around and sing along to everything from Outkast's "Hey Ya" to the rock band's own "Numb", is a spinoff of the popular bit from James Corden's "Late Late Show".
"In memory of Chester Bennington: March 20, 2017 - July 20, 2017".
Chester Bennington, pictured performing during KOMP'S Totally Politically Correct Holiday Bash at The Joint inside the Hard Rock Hotel & Casino on December 15, 2013 in Las Vegas, appeared in good spirits just days before his death, filming "Carpool Karaoke" with his Linkin Park bandmates. It ends with a link to the One More Light Fund, which the band established to honor Bennington.
Bennington's bandmates from Linkin Park will host a benefit in his memory October 27 at Hollywood Bowl in California.