"I know your spirit is still present, and your essence still lives on in the hearts of many," Guzman wrote.
"She’s standing [there] like, 'You're an a**hole.' I'm like, 'What? I'm explaining factually like what I'm doing.'"
Holker will be a judge alongside Jojo Siwa and Maksim Chmerkovskiy.
Lythgoe announced his departure from the show earlier this month following Paula Abdul's sexual assault allegations against the longtime judge.
Holker honored her late husband with a post featuring pictures of herself and their children at his grave.
"I’m feeling this much pain because I’ve had so much love," Holker Boss said.