The man who took the photo of the Skittles has also hit back, telling BBC that he was a refugee.
"This was not done with my permission, I don't support his politics and I would never take his money to use it," UK resident David Kittos told the BBC.
Mr Kittos posted the image to his Flickr account and was surprised to see it being used by Donald Trump Jr.
"In 1974, when I was six-years old, I was a refugee from the Turkish occupation of Cyprus so I would never approve the use of this image against refugees."
The Skittles saga has also been criticised by others for detracting attention away from news that Trump used funds from his charitable foundation to pay settlements in legal cases involving his businesses.
"If you are covering Skittles-gate instead of Trump's illegal use of his foundation, you are probably in journalism for the wrong reasons," tweeted Dan Pfeiffer, a former top adviser to President Barack Obama.
The Washington Post revealed on Tuesday that the cases involved a combined $258,000 paid out by the Donald J. Trump Foundation - a charity almost entirely funded with other people's money, the newspaper said - and follows a review of legal documents and the foundation's tax records.
The newspaper carried out a weeks-long investigation into the charity's finances, finding that Trump himself has not contributed a dollar to since 2009. The group is funded by donations from third parties instead.
One of the group's suspect payments was a $100,000 donation to a veterans' charity in 2007 as part of a legal settlement with the city of Palm Beach, Florida.
Trump had sued the city after it fined him $120,000, or $1250 per day, for erecting an 80-foot (24m) flagpole at his Mar-a-Lago Club that exceeded the maximum 42 feet permitted by local regulations.
The Trump Foundation also made transactions that appeared to be exclusively for the benefit of the real estate mogul or his businesses, apparently in violation of regulations governing charities, the Washington Post said.
In one case, the charity paid $20,000 in 2007 for a six-foot portrait of Trump, the newspaper reported.
"Clearly the Trump Foundation is as much a charitable organisation as Trump University is an institute of higher education," said Christina Reynolds, a spokeswoman for the campaign of Trump's White House rival, Democrat Hillary Clinton.
"Once again, Trump has proven himself a fraud who believes the rules don't apply to him," she said in a statement.
"It's past time for him to release his tax returns to show whether his tax issues extend to his own personal finances." Some Democrats have complained that the media has not sufficiently reported about the Trump Foundation's suspected wrongdoing, accusing journalists of being lenient in their treatment of the outspoken billionaire.
Trump's campaign denied the Post report.
"In typical Washington Post fashion, they've gotten their facts wrong. It is the Clinton Foundation that is set up to make sure the Clintons personally enrich themselves by selling access and trading political favours. The Trump Foundation has no paid board, no management fees, no rent or overhead, and no family members on its payroll," said spokesman Jason Miller.
