The Australian government spent more than $10,000 in taxpayer cash fighting a legal battle to keep documents secret about the home affairs minister Peter Dutton’s decision to save two foreign au pairs from deportation.

The visa status of the two unknown young women has been in the spotlight since March, when it was revealed that Dutton used his powers of ministerial discretion to grant them visas on public interest grounds.

In the first case, an au pair whose visa was cancelled at Brisbane’s international airport in June 2015 was able to make a phone call and within a couple of hours the minister approved a new visa.

In November the same year, Dutton defied written warnings from his own department that granting a visa to a second au pair was of “high risk” because she had been previously counselled about work restrictions.

Dutton insists he doesn’t know the two individuals involved and that they didn’t work for his family.

Overnight the department released answers to 28 outstanding questions from a May Senate estimates hearing, which were close to a month overdue.

At the May hearing, the Labor senator Murray Watt grew increasingly frustrated with the department’s obfuscation and said: “It feels like a cover-up.”

Watt had asked home affairs department secretary, Michael Pezzullo, who the first au pair had phoned while detained at the airport in order to receive ministerial intervention.

“This is a matter for the individual and not the department,” the department responded in its written answer.

The department said it was unable to calculate the number of cases with similar circumstances in which tourists have been allowed to stay in Australia despite suspicions they would undertake paid work.

“Determining the number of times this has occurred would require an examination of a large number of individual cases and an unreasonable diversion of departmental resources,” the department said.

Guardian Australia has spoken with a German au pair who was stopped at Sydney’s international airport in 2012 and had her visa cancelled at the border because of concerns she would work. She was locked up for a night at the Villawood detention centre and was promptly put on a plane the next day to Thailand.

“All in all, I think it’s the worst experience till now that I’ve had in all my travels,” she said.

The department refused to be drawn on questions about whether a Liberal party contact had made a call to the minister’s office seeking ministerial intervention for the au pair or whether the person was known to the minister.

It also revealed it had not undertaken any monitoring to ensure the June au pair had complied with work restrictions.

The total legal cost associated with the department fighting a freedom of information case to suppress documents about the au pairs was $10,245.92.

Dutton received departmental briefings about the case three days after a federal tribunal hearing in March and twice in April after the tribunal ruled in the department’s favour based on concerns for the au pairs’ privacy.