The policy started in El Paso, Texas, according to two Customs and Border Protection officials.

Immigrant advocates had braced for the court-ordered relaunch, but despite commitments by the Biden administration to be transparent, advocates told CNN they remained frustrated amid further confusion.

Under the Trump administration, thousands of migrants were subject to the program, formally known as Migrant Protection Protocols, and resided in makeshift camps along Mexico's northern border often in squalor and dangerous conditions.

President Joe Biden pledged to end the program and began the process of admitting those migrants who had previously been subject to it. But a federal judge in Texas disrupted those plans when he ordered the administration to revive the policy.

The Biden administration had pledged to make important changes as part of the restart, such as improving access to lawyers. Currently, there is a limit of 30 people enrolled in the policy per day in El Paso, according to Customs and Border Protection. Enrollments are expected to increase, as the policy expands to other locations along the US-Mexico border, including in San Diego, Calexico, Nogales, Eagle Pass, Laredo, and Brownsville.

White House press secretary Jen Psaki said Monday that the Biden administration was not eager to move ahead with the program, telling reporters Monday that DHS put in place changes to "improve humanitarian components," but added the administration still feels the program is "inefficient, inhumane."

"We did not eagerly reimplement it," Psaki said.

Those changes haven't quelled concerns among advocates.

"It's lipstick on a pig. But it's still a pig," said Sue Kenney-Pfalzer, director of border and asylum network at HIAS. "MPP is just plain inhumane. It's a little less inhumane perhaps, but it's still inhumane. Now that it's here and we have no choice we're going to figure out a way to get services to people."

HIAS, along with other groups, refused to be included in a list of legal service providers put together by the Biden administration, arguing that it didn't want to be complicit with the return of the policy.

Everyone in the new program will have access to an attorney before and during their interviews about fear of returning to Mexico, as well as prior to court hearings in the US, according to the Department of Homeland Security, marking a change to how the policy previously operated.

But attorneys say it's still unclear how migrants will reach them and whether they have enough capacity to serve those who are subject to the policy.

"We have huge capacity limits and don't want to be complicit in the restarting of MPP," said Linda Rivas, an immigration attorney and executive director of Las Americas Immigrant Advocacy Center. "When they rely so much on the NGOs to make things happen, they try to justify programs that are inhumane and don't restore asylum."

Asylum officers from Houston and Los Angeles field offices have been trained on the new "Remain in Mexico" policy, according to a Homeland Security official, who added trainings for other officers will occur throughout the week.

"DHS is closely coordinating the court-mandated reimplementation of MPP with the Government of Mexico to address security concerns and operational constraints. DHS began the court-mandated reimplementation in one location today. For operational security reasons, DHS is not sharing details such as location of initial returns or number of individuals enrolled," a Homeland Security spokesperson said in a statement Monday.

Last week, the union representing US Citizenship and Immigration Services asylum officers released a letter calling the Trump-era program "irredeemably flawed."

"No matter how you improve this, it's still fundamentally wrong and violates our convention mandate," said Michael Knowles, a representative of the American Federation of Government Employees National CIS Council 119, referring to the international refugee convention's prohibition on returning refugees to a territory where their lives or liberty may be at risk.

In a statement, the Round Table of Former Immigration Judges, which consists of 51 former immigration judges and members of the Board of Immigration Appeals, criticized the Biden administration for resuming the controversial policy.

"Tragically, to comply with a most misguided court order, the Biden administration, which promised us better, is today not only resuming the program with most of its cruelty intact, but expanding its scope to now apply to nationals of all Western Hemisphere countries," the statement reads.