"Couldn't be more excited," he said in the video. "Can't wait to get the tan on, get some heat on me after being in Melbourne for a few weeks."
He then pointed at his Bowyer before adding: "I'm going to be dark, (but) she'll be darker, like an Aborigine!"
The video then abruptly ends and it appears that Bowyer quickly cut the clip.
Indigenous activist Tarneen Onus-Williams, shared the video on Twitter and branded Delmege's comments "disgusting".
"The fact he's laughing about being Aboriginal is disgusting," she said in the post — which was commented on by dozens of outraged followers.
Delmege and Bowyer unveiled their romance last month and recently moved in together in Melbourne.
The unlikely couple broke their silence late last month after finding love on Married At First Sight where they had each been paired with separate partners — and finally addressed claims Troy was a virgin prior to the show.
While discussing her 35-year-old brother's quirky traits in an interview with NW, Tanya Delmege revealed that as far as she knew, "he's on the V-plates".
Speaking to Kyle and Jackie O following the reality TV show's explosive finale, Troy said Carly "popped my cherry".
Kyle pressed him on whether or not he'd actually been a virgin before signing up for the show, but Troy deflected with jokes.
Meanwhile, a shocked-sounding Carly jumped in, telling them: "It's news to me."
Afterwards, Troy finally explained the rumours weren't true, but admitted: "It would have been nice to have waited for such a beautiful girl."