Special counsel Jack Smith's office is continuing to investigate whether two employees of Donald Trump gave false testimony to a grand jury as part of the criminal probe into the former president's retention of classified documents at Mar-a-Lago, prosecutors revealed in a court filing Tuesday.

The filing provides the most direct explanation of how prosecutors obtained information used in the superseding indictment.

Prosecutors believe that Yuscil Taveras, an IT worker who has not been charged, and Carlos De Oliveira, the property manager of Mar-a-Lago charged alongside Trump, gave false testimony about alleged efforts to delete incriminating security camera footage from the Florida club, according to the filing.

They say that Taveras -- referred to in court documents only as "Trump Employee 4" -- repeatedly "denied or claimed not to recall any contacts or conversations about the security footage at Mar-a-Lago" despite evidence to the contrary. De Oliveira allegedly told prosecutors the same.

But more recently, after switching lawyers, prosecutors say that Taveras changed his story about efforts by Trump, De Oliveira and their other co-defendant, Walt Nauta, to delete security footage.

Both Taveras and De Oliveira are now being investigated for their earlier statements, prosecutors revealed in the filing.

De Oliveira and Nauta, Trump's aide, are charged with making false statements about whether they saw boxes containing classified documents being moved around Mar-a-Lago during voluntary interviews with the FBI. They, along with Trump, have pleaded not guilty.

Tuesday's filing came in a dispute between prosecutors and Nauta's attorney over how the court should handle what Smith said is a conflict of interest in Nauta's representation. Prosecutors have flagged to the court that Nauta's attorney has represented two witnesses who will likely testify in any eventual trial.

Taveras and Nauta were both previously represented by attorney Stanley Woodward. Prosecutors had argued that created a conflict of interest because if Taveras amended his testimony about efforts to delete the security footage, he would incriminate Nauta.

When Taveras was advised of the conflict, the filing says, he switched to a public defender. Prosecutors allege that's when Taveras changed his story. Many of the details he gave were used in the superseding indictment in the case, and if he were to testify at trial, prosecutors point out that Taveras would be cross-examined by his former lawyer.

In a court filing last week, Woodward pushed back on prosecutors' allegations that his previous representation presents a conflict and told the court that it should take a narrower approach to dealing with the issue than the broad conflict hearing that prosecutors are proposing.

He declined to comment to CNN.