The two's conversation began over talk on whether Stefanovic should wax his eyebrows.
"If you want to see Georgie wax Karl on Monday morning, send us an e-mail!" Karl said excitedly.
Georgie then preceded to jokingly whack Karl across the chest and replied, "Oh wax! As in whacks!"
"Not axe!" Karl quickly replied.
"Apparently you've already been axed!" Georgie said, laughing.
"Gone! A couple of weeks ago! Don't mention the war!" he joked, pretending to cry.
Earlier this month, Stefanovic has addressed reports that his position at the Today Show is at risk following Channel Nine CEO Hugh Marks comments blaming the hosts personal life for the breakfast programs plummeting ratings.
On Wednesday's program, the 44-year-old journalist made a thinly veiled reference to the media speculation during a segment about tonight's Dally M Awards.
Sports reporter Tim Gilbert criticised an article that claimed Sam Burgess was skipping the NRL ceremony in the wake of his sexting scandal, of which he was cleared.
Karl took the opportunity to attack the media.
"There is so much garbage that gets written about this desk. They [journalists] make it up," said a clearly worked-up Tim.
"I think you've just got to ignore it,' Karl replied, before Tim added, 'Do you?"
"It's upsetting. It's upsetting to have stuff written about you, isn't it?" Karl then added, before bursting out laughing.