The Kiwi heavyweight has used the cruel jibe from British talk show host Graham Norton and picked up by Joshua as motivation for his preparations for their world heavyweight unification fight.
WBO champion Parker tangles with WBA and IBF champion Joshua in Cardiff on April 1 (NZT) and the 26-eyar-old is determined to be in the shape of his life.
Five weeks into his Las Vegas training camp, the signs are promising with Parker quickly losing weight and regaining his trademark speed.
Parker's trainer Kevin Barry is delight with what is unfolding in front of him as the clock rapidly counts down to what could be New Zealand's biggest sporting moment of 2018.
"Joe has been very disciplined and on point. His body looks really good. He is in much better shape already than he was for the Hughie Fury fight," Barry told Stuff.
Barry said Parker had taken the taunts from Norton and Joshua on the chin.
"He laughed at it. He didn't take it as an insult, he thought it was a fair cop, he'd put a few pounds on in his break. Joe likes a pie but I can tell you this, he hasn't eaten any pies in the last five weeks.
"He's doing some great strength and conditioning work, I'm confident we are on track for a very good performance.
"Joe looks good, he's going to look even better when he gets on the scales for the weigh-in and I think he will be ready for a career-defining performance in his biggest ever challenge."
Parker might never have the ripped physique of gym-bunny Joshua but he has never turned up for a fights embarrassingly out of shape during a run of 24 wins and prides himself on his appearance. Barry concedes Parker's 112kg weight against Fury last September was too high and wants him back around 108kg for Joshua.
"There's a lot more firepower coming out of him for this fight. I need a lot of movement and I need a lot of punches off Joe and his fitness levels need to be a lot greater than his last fight because the challenge is so much bigger."
Barry and Parker haven't tried to reinvent their programme given it has worked well over a five-year unbeaten run. But they have tweaked things. There's extra yoga, more pad work, a new strength and conditioning coach and a new massage therapist all helping to prime the fighter.
Barry likes how that is transferring into the ring as they eye the final three weeks of sparring before transferring to the UK for a two-week tapering ahead of fight night.
"Joe has adopted our game plan very well and he's showing it to me in sparring. I think the last couple of sparring sessions have been our best for some time so it's all coming together nicely," Barry said.
It's no easy task trying to imitate Joshua but Barry says Parker's workhorses are producing "some very good work".
"They are doing the Anthony Joshua thing as well as they can. They are throwing the combinations I need them to throw, combinations that I have identified as the strengths of Joshua.
"It might be fair to say there is only one Anthony Joshua out there. But as far as hand speed is concerned, I'd say there is only one Joseph Parker out there as well. So I think both guys have got challenges to replicate things in sparring."
Parker is also juggling a busy media schedule as the international focus intensifies, determined not to let that affect his training or rest and recovery.
"It's all going well ... we are right on track, no excuses," Barry said.
"We both believe this is the right time to fight Anthony Joshua. If we don't get the result that we thing we are going to get, it's because we're simply not good enough. There is no other reason. If we don't beat him, it's because he is the better fighter.
"But we are both very confident, we like where we are at, we are excited by the magnitude of this challenge. I've said all along, the bigger the challenge will bring the best out of Joseph."