Updated March 12, 2022 at 9:04 AM ET

A woman who fled Ukraine with her three young children tried to cross the border between Tijuana and San Diego earlier this week — only to be turned away under sweeping pandemic border restrictions.

Thursday, U.S. immigration authorities relented, allowing the family to enter the country and seek asylum.

But immigrant advocates say their story underscores the cruelty of restrictions put in place at the beginning of the pandemic by the Trump administration.

"The fact that we're using COVID as an excuse to keep out asylum seekers at this moment in time, it's just becoming more and more absurd and untenable for the administration," said Blaine Bookey, an attorney at the Center for Gender & Refugees Studies, who is representing the Ukrainian family.

For more than a year, the Biden administration has quickly expelled migrants at the southern border under the controversial public health order known as Title 42 — despite repeated calls from Democratic lawmakers and immigration advocates to end the Trump-era policy.

Those calls have grown louder this week as Ukrainians fleeing the Russian invasion of their country began to arrive at the U.S.-Mexico border and a pair of court rulings on Title 42 put additional pressure on the Biden administration to make a decision about its future.

"This is not who we are as a country," Senate Majority Leader Chuck Schumer (D-NY) said during a call with reporters on Thursday. "Continuing this Trump era policy has defied common sense and common decency. Now's the time to stop the madness."

The Biden administration announced late Friday that it would officially end Title 42 for children crossing the border without their parents or legal guardian, but left the policy in place for other migrants.

When Title 42 began nearly two years ago, immigration authorities used the policy to quickly expel all migrants they encountered — without giving them a chance to ask for asylum protection or other protections under U.S. law.

Shortly after taking office, the Biden administration exempted unaccompanied migrant children from the policy. It has also allowed many migrant families to seek asylum in the U.S.

For a while, the Biden administration was talking with immigrant advocates about ending Title 42 but abandoned that idea as the number of migrant apprehensions at the border soared to record levels last year.

Instead, the Biden administration kept Title 42 in place, and defended it in court as necessary to prevent the spread of COVID -19. Immigration authorities have continued to enforce the policy for single adults and some families, expelling migrants well over a million times since Biden took office.

The Department of Homeland Security insists that Title 42 is a public health measure, not an immigration policy. DHS says it's up to the Centers for Disease Control and Prevention to decide when the order should be lifted, and that no such decision has been made.

The latest order from the Centers for Disease Control and Prevention is set to expire in early April. But immigration hardliners warn that lifting Title 42 restrictions now could lead to another surge in migrant apprehensions this summer.

Still, the Biden administration is under growing pressure to end the policy because of a pair of court rulings.

First, a D.C. Circuit of Appeals panel ruled that the administration cannot use Title 42 to send migrant families back to places where they could face persecution or torture.

"The CDC's order looks in certain respects like a relic from an era with no vaccines, scarce testing, few therapeutics, and little certainty," wrote Judge Justin Walker, a Trump appointee, on behalf of the three-judge panel.

Immigrant advocates hailed the ruling as a win because it suggests that all migrants should receive a screening and a chance to seek protections in the U.S. But it's not clear how those screenings would work in practice.

In the second case, a federal judge in Texas ruled that the Biden administration acted arbitrarily when it decided to exempt unaccompanied migrant children from Title 42.

In the second case, a federal judge in Texas ruled that the Biden administration acted arbitrarily when it decided to exempt unaccompanied migrant children from Title 42. That ruling caused worry among immigrant advocates that the administration would begin expelling unaccompanied children as soon as Saturday.

Instead, the Centers for Disease Control and Prevention announced that it is terminating the government's authority to expel unaccompanied children.

"In the current termination, CDC addresses the court's concerns and has determined, after considering current public health conditions and recent developments, that expulsion of unaccompanied noncitizen children is not warranted to protect the public health," the agency wrote in announcing the order.

In a separate 21-page order justifying the termination, CDC director Rochelle Walensky noted the "unique vulnerabilities" of unaccompanied minors.

Advocates hailed the CDC's decision — but urged the administration to go farther and scrap Title 42 altogether.

Advocates say the Biden administration has expelled tens of thousands of migrants back to Haiti and other countries where their lives could be in danger.

"We are asking to revoke Title 42 and welcome people, whether they are coming from Ukraine, Haiti, Cameroon, Central America," said Guerline Jozef, the executive director of the Haitian Bridge Alliance, during the call with reporters on Thursday.

That includes the Ukrainian woman who sought asylum this week in California. Her lawyers say the 34 year-old mother, who asked to be identified only as Sofiia, is trying to reach her family members who are U.S. citizens living in California.

Blaine Bookey said she happened to be in Tijuana to work with Haitian migrants who are also seeking asylum in the U.S. when she noticed Sofiia and her children near the port of entry.

"We're extremely happy for Sofiia and her family that she's going to have the chance to seek safety," said Blaine Bookey. "But at the same time, it shouldn't be this hard for families to be able to find safety."

Immigration lawyers in Tijuana say they've seen more Ukrainian families gathering outside the border crossing this week, hoping that they too will get a chance to apply for asylum.

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