GE's CEO, John Flannery, told Garden "everything is on the table. There are no sacred cows. Hopefully, that company will start to run the right way and the board will get more active," Peltz said in an interview with CNBC's "Squawk on the Street." "I think Ed is going to bring a fresh mindset into that boardroom."
Trian, which was co-founded by Peltz and Garden, had a $1.68 billion stake in General Electric as of June 30, according to FactSet, and has been pushing the company to make changes.
Garden was named to GE's board on Monday,
"People were probably nervous,' Peltz said. "When the CFO quickly departs, people get nervous, and I can understand that."
General Electric's stock has dramatically underperformed the Dow Jones industrial average this year, falling 25 percent. The Dow, meanwhile, has surged 15.3 percent.
Correction: GE announced the departure of several top executives. A previous version of this story mischaracterized some of them as board directors.