"Why did @FLOTUS wear this tone-deaf jacket boarding the plane for this trip, allegedly to show she cares about the kids in these detention facilities?!" another person questioned.
"It's a jacket. There was no hidden message", first lady communications director Stephanie Grisham said in a statement.
Images of the first lady wearing a green parka jacket from high street chain Zara with the message written in white lettering have emerged.
Melania Trump's visit to the border came a day after her husband signed an executive order stopping his own administration's policy of separating children from their families, which had led to widespread criticism from voices on both sides of the aisle. "She wants to see a realistic view of what's happening". On Wednesday, Trump made a rare retreat, signing an executive order that he said would end family separations as Congress prepared to consider legislation that would force a halt to the policy.
Trump had come under pressure to stop the practice, including from GOP allies and the first lady herself, following a public outcry sparked by widespread images of children held in fence-like structures.
Grisham is referencing the backlash that exploded when the first lady was mocked for wearing sky-high stilettos as she headed to Texas after Hurricane Harvey in August. The trip was announced Wednesday before Trump's decision. The first lady is traveling to Texas to see first hand the condition and treatment that children taken from their families at the border were receiving from the federal government.
Mrs Trump, sitting with officials at a centre in McAllen, Texas, said: "How can I help these families reunite with their children as quickly as possible?"
Mr Trump said yesterday as he signed an order to scrap the policy: "It's about keeping families together while at the same time making sure that we have a very powerful, very strong border".
New York City Mayor Bill de Blasio, a Democrat, revealed how he was shocked to learn that more than 200 children who were recently separated from their families at the southern border are now at an immigration foster care center in his own city - and nobody told him.
Asked if they had any reaction to the charges against them being dropped, he said, "They're asking about their children, frankly".