The official Trump War Room account on Twitter posted the altered front cover of the magazine on Wednesday, the same day the 16-year-old won the accolade for “turning vague anxieties about the planet into a worldwide movement calling for global change”.
Mr Trump’s team said: “When it comes to keeping his promises, there’s only one Person Of The Year.”
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Listing the reasons why they believe he deserved the award, they added: “Booming Economy, Record Job Creation, Historic Tax Cuts, #AmericaFirst Trade Deals, Isis Destroyed, Building the Wall.”
The US president mocked Greta after she received the recognition, tweeting on Thursday: “So ridiculous. Greta must work on her Anger Management problem, then go to a good old fashioned movie with a friend! Chill Greta, Chill!”
Mr Trump’s son, Donald Trump Jr, also took issue with Time‘s decision, instead suggesting pro-democracy protesters in Hong Kong who were “fighting for their lives and freedoms” instead of Greta, whom he described as “a teen being used as a marketing gimmick”.
It comes after Mr Trump’s campaign team depicted the president as Marvel villain Thanos.
They posted a video showing Mr Trump’s face superimposed on the body of the superhero’s nemesis in a scene from the film Avengers: Endgame, which features the character saying “I am inevitable” before snapping his fingers in an attempt to wipe out all life in the universe.
The video then cuts to Nancy Pelosi and other Democratic leaders disintegrating into dust.
The US president previously posted a photo on Twitter showing his face on the shirtless body of Sylvester Stallone in the Rocky films.
He posted the image after claiming during a campaign rally in Florida that a doctor had told him to “show us that gorgeous chest” during a medical exam.
On Wednesday, Greta used her address at the UN’s annual climate summit to accuse governments and businesses of misleading the public by holding talks that she said aren’t going to stop the world’s “climate emergency.”
“The real danger is when politicians and CEOs are making it look like real action is happening, when in fact almost nothing is being done, apart from clever accounting and creative PR,” she said.
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Mr Trump was named Time‘s Person of the Year in 2016.