But Willis appeared unfazed by the comments.
The contentious report won't be publicly released.
There is anger in the National Party membership over the tightly held review.
Collins said "wokester" was not a term she would ever use or think of.
Collins admits she led the party to a "big, fat stonking loss" at the election - but maintains her job is safe.
Collins' gave her first speech of 2021 on Tuesday.
Falloon resigned as MP for Rangitata in July.
The petition has received more than 39,000 signatures.
"It's time to put the health of young Kiwis first."
