Sri Lankan couple Priya and Nades Murugappan and their Australian-born daughters Kopika and Tharunicaa, aged four and two, are detained on Christmas Island ahead of a Federal Court challenge due to begin on Friday.
Priya, Nades and Kopika have been refused refugee status and the court fight hinges on Tharunicaa and her right to apply for protection.
In a pre-hearing matter on Monday, Justice Mark Mochinsky said he had started reading documents filed on behalf of Immigration Minister Peter Dutton.
"There does seem to have been some over-enthusiasm with the redactions," he said.
The issue was raised by Tharunicaa's lawyer, Angel Aleksov, who noted issues with redactions to two documents he received late on Sunday night.
One document was a ministry briefing between the Immigration Department Secretary and Mr Dutton from mid-July last year.
The other was a document "wholly blacked out", which he said appeared to involve some engagement between Australia and Sri Lanka.
Justice Mochinsky also noted concerns that the surnames of people within the department had been redacted.
"I was having a little trouble piecing together who was who," he said.
After negotiations failed, Jonathan Barrington for the minister revealed a request that the information be protected because it related to foreign relations.
Justice Mochinsky read the unredacted documents and said he was inclined to agree, but reserved his final ruling until the hearing in case the redacted matters become relevant.
He also asked Mr Barrington for further information, which he posed as a hypothetical rather than specific to this case.
The judge noted that sometimes people might raise concerns about returning to a country where their views oppose that of the government, but the tribunal rules the fear is not justified because the government does not know that individual.
He questioned whether that ruling would change when there has been direct dealings between the Australian government and the foreign government about the return of particular people.
Mr Barrington said he expected that was something to be addressed in documents to be filed before Friday.
The hearing is scheduled for two days.