Donald Trump defended his wife, saying the reference was her response to the "Fake News Media".
"I'm here to learn about your facility", she said as she received a briefing about the work of Upbring New Hope Children's Shelter.
Her spokesperson, Stephanie Grisham, said of the border visit: "She wanted to see everything for herself".
Melania's visit to McAllen comes amid the bipartisan backlash over the Trump administration's enforcement of a "zero-tolerance" policy - criminally prosecuting migrants who cross the US-Mexico border.
When Melania Trump met with detained children at the Texas border on Thursday, she struck a compassionate tone, asking staff at the facility: "How I can help. these children to reunite with their families as quickly as possible?"More news: U.S., China sink into deepening trade conflict
You could argue that Trump really tipped her hand when she wished the foster children "good luck" upon exiting the facility.
President Trump supported this trip but he didn't send her.
The question now is what effects the separations will have on the young children. But her message and the carefully crafted visuals showing a first lady rushing to the scene of a crisis touching the lives of children were soon obliterated by other words and images. She is aware of the message she is sending, which is typically one of aspirational luxury.
"You are a First Lady for Gods sake walking around with a jacket that says 'I really don't care.' This can't be for real".
After staying quiet as global outcry grew over the Trump administration's family separation policy, Ivanka Trump on Thursday also called on families to be "swiftly" reunited. "Melania has learned how dishonest they are, and she truly no longer cares!" he tweeted. The trip was meant to lend support to those children who remain separated from their parents, said Grisham. "We don't want to have people - we don't want to have children separated from their parents", the President said.More news: Italy's interior minister turns gaze to 'Roma question'
Mrs. Trump, whose focus is on children, may have helped encourage her husband to act. The kids she was visiting are the children separated from their parents by immigration officials under a new policy that's been described as "nothing short of torture", and the world has been absolutely up in arms about it for the past week.
Critics were quick to attack the first lady's fashion choice, calling it insensitive.
During her visit to the Upbringing New Hope Children's Shelter, Melania said 'I'm looking forward to meeting the children'. The other children were placed there after they crossed into the USA alone.
It's not known whether someone on the plane noticed the phrase before she arrived in McAllen, Texas.
Mrs Trump left the White House quietly in the morning and flew to Texas for the unannounced visit, a day after Mr Trump signed an executive order keeping families intact who cross into the United States illegally from Mexico.More news: Oil falls as Opec nears deal to raise production
She also spoke with staff members, and inquired about the children's well-being.