Businesses that applied for refunds of President Trump's "liberation day" tariffs, which the Supreme Court struck down in February, are getting some clarity on when they will receive their money. 

The Trump administration is expected to issue the first tariff refunds as early as May 11, according to court documents filed this week. The White House is estimated to have collected $166 billion in duties that it now owes back to importers. 

The federal government on April 20 launched a portal where businesses could file refund requests for Mr. Trump's International Emergency Economic Powers Act, or IEEPA, tariffs. Called CAPE, or the Consolidated Administration and Processing of Entries tool, the portal briefly crashed when a large number of businesses visited the site after its debut.

The portal has since been working as intended for most businesses, with some legal experts praising how quickly the U.S. government created the refund mechanism.

U.S. Court of International Trade Judge Richard Eaton, who oversees the tariff refund process, said in a filing Tuesday that the first tranche of refunds could land in businesses' bank accounts around May 11.

Judge Eaton said that U.S. Customs and Border Protection has accepted roughly 21% of IEEPA duty refund requests. Of those, 3% are already in the "refund stage of the process," Eaton said. The first refunds, which will come from the U.S. Treasury Department, will arrive as early as May 11.

In his filing, Eaton acknowledged some of the hurdles businesses faced in navigating the tariff refund process. Some importers said they were unable to access their Customs importer accounts and waited on hold for hours trying to resolve administrative errors. 

Beth Benike, co-founder of Busy Baby, a Minnesota-based maker of baby accessories, is among the U.S. small businesses that have not yet been able to apply for tens of thousands of dollars in refunds due to portal access issues. 

Dahlia Rizk, owner of Buckle Me Baby, a Massachusetts-based kids' outerwear company, also reported struggles applying for $66,000 worth of refunds she's owed.

"It was very difficult. I had a lot of trouble," she told CBS News. "I shouldn't have had to call up Border Patrol and explain my entire life story." Ultimately, she was able to submit a request that she said Customs has approved and expects to receive in the coming months.