Annie Scott, left, and Fernanda Kock wear "I Really Do Care" shirts at Saturday's rally in New York.
CNN  — 

The White House says Melania Trump wasn’t sending an immigration message with her “I Really Don’t Care” jacket. But demonstrators who riffed on it Saturday sure were.

Protesters at immigration rallies across the country held or wore slogans suggesting the opposite message: “I really do care.”

A woman holds a "Yes Melania I do care" sign at an immigration rally Saturday morning in Miami.

In New York, protesters Annie Scott and Fernanda Kock wore olive green T-shirts with the message “I Really Do Care” on the front.

“We’re here because we think this is important,” Scott told CNN about attending the rally to protest the White House’s “zero tolerance” immigration policy.

The “I Care” messages recall first lady Melania Trump’s recent wardrobe choice. Boarding a plane last week to see an immigrant children’s shelter in Texas, she wore an olive Zara jacket with “I Really Don’t Care. Do U?” in graffiti-style lettering on the back.

Trump didn’t wear the jacket at the facility, and her spokeswoman insisted the first lady wasn’t conveying a hidden message. But critics complained her clothing choice was insensitive, given her destination and the ongoing national debate over immigrant family separations.

Thus, the “I Really Do Care” symbols on display Saturday.

The Ickowitz family takes part in Saturday's Washington rally. They are, from left to right, Mike, 39; Jake, 9; Tanya, 40; and Rachel, 12.

In Washington, four members of the Ickowitz family donned green shirts with the spinoff message.

Mike Ickowitz, 39, of Knoxville, Tennessee, said he believed the first lady’s messaging was deliberate, so he and his family were “sending one right back” during a rally near Lafayette Square, blocks from the White House.

“We have to speak for the marginalized” people, his wife, Tanya, said.

"Separating families, especially young children, without a plan to reunite them is abhorrent," Margaret Stokes said at Saturday's rally.

Also in Washington, Margaret Stokes, a 54-year-old teacher from Virginia, held a sign depicting a baby’s onesie, printed with the words, “Where Is My Mother?” Below it was the message, “Do You Care?”

“Separating families, especially young children, without a plan to reunite them is abhorrent,” Stokes said. “This is not America.”

CNN’s Sarah Jorgensen contributed to this report.