Mrs Trump was spotted in the coat, which featured graffiti writing on the back with the words "I really don't care do u?", as she boarded a plane.
Her spokeswoman said "there was no hidden message" in the former fashion model's sartorial choice.
The $39 (£29) jacket from Zara caused an uproar on social media.
US President Donald Trump later tweeted his wife's coat "refers to the Fake News Media".
Hours after the photo of her departure outfit went viral, she again donned the jacket to disembark from the plane at an Air Force base outside Washington DC.
She ignored questions from reporters as she entered the presidential motorcade.
Mrs Trump's spokeswoman Stephanie Grisham lambasted US media on Twitter for focusing on her fashion choice.
Mrs Trump was not seen wearing the coat when she first arrived in Texas, but had it on again when she returned to Washington DC.
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Pretty tone deaf
Katty Kay, BBC World News presenter, Washington
Melania Trump's empathetic visit to the Mexican border risks being overshadowed by the unempathetic message on the back of her coat.
It stretches credulity that the first lady would make the effort to fly down to Texas, visit children, talk to staff and engage in this heartbreaking story only to deliberately undermine it with a callous choice of clothing.
It's not clear how this was allowed to slip through the careful White House protocols but it's a mistake on the part of her staff.
I give her the benefit of the doubt on compassion - but if she chose to wear this without thinking, it was pretty tone deaf.
