In a statement to SBS News, Mr Dutton said he made "decisions on the merit of individual cases according to the law".
A Senate inquiry into the matter began on Wednesday, with a final report due by 11 September.
What exactly is an au pair?
An au pair is usually defined as a domestic assistant from another country whose main role is to assist a family with childcare and some household tasks.
The translation from French means "on par" or "equal to" as the au pair lives with a host family, receiving accommodation and an "allowance" in exchange for their work.
To calculate the allowance, families are advised to use the national minimum wage, which amounts to $18.29 per hour of work, minus the average cost of "room and board" (typically $350 per week).
According to material from industry body the Cultural Au Pair Association of Australia, au pairs generally care for a family's child or children for 20-40 hours per week.
Laurie Berg, a senior lecturer in the Faculty of Law at the University of Technology Sydney, told Fairfax last week that there were as many as 10,000 au pairs in Australia.
What does the job involve?
Australian au pair agencies tend to target young women.
"You will be the envy of all your friends! They will follow you online, read about your adventures, the places you go and the people you meet! You will be living the Australian dream!" one agency website says.
Another asks: "would you like to experience a foreign culture in a personal, protected and enjoyable way? Make friends for life while improving your English and enhancing your CV all with the help of an amazing host family!"
Some websites have detailed descriptions of the host family's set-up and work they will be expected to do.
Source: Aussie Au Pair Services
One says: "we need the au pair to assist with getting the children ready for school; helping prepare their breakfast; cleaning up after breakfast; walking eldest to school; attending playgroup or paint and play or story time at the library, preparing lunch for children, bathing children, reading story to kids".
Why do people work as au pairs?
Au pair agencies trumpet the benefits of the arrangement for both international visitors and the host family.
Nicole Kofkin, chief executive of Australian agency Smart Au Pairs, told SBS News the program "provides an opportunity for a young person with limited previous work experience to be assured of a safe and welcoming family where they can live and work at the same time".
"Many are keen to improve their English skills during the placement and become fluent in a matter of months."
It is a point echoed by the founder of fellow Australian agency AIFS, Wendi Aylward.
"For many young people, the uncertainty of going overseas for the first time and not knowing whether you have a job [can] be a daunting prospect," Ms Aylward told SBS News.
"[Also], more and more young people are wanting to immerse themselves in a culture instead of staying in a hostel and having a peripheral experience ... They want to live with an Australian family, they want to know what it's like to experience the Australian lifestyle."
Do they need any qualifications or checks?
Au pair placements are either arranged informally or through an agency. Certain agencies will screen the au pair and the family prior to offering a placement, but there is no consistent approach.
Some conduct a police clearance check of the family and ask for qualifications or experience of prospective au pairs but "agencies range greatly in their screening processes and level of support during the placement," the Cultural Au Pair Association of Australia says.
"Under the current model, it is possible for an au pair and family to be matched without any screening."
A study UTS's Ms Berg undertook in 2017 said Australia "has one of the least regulated au pair sectors in the world".
What visas do au pairs need?
Individuals wanting to work as an au pair must hold a valid work visa.
"There is strictly no au pair work allowed on a tourist or visitor visa," Julie Williams, a senior registered migration agent at Migration Downunder, told SBS News.
Australia does not have a dedicated au pair visa. Instead, individuals need to apply for a Working Holiday Visa (Subclass 417) or Work and Holiday Visa (Subclass 462). Both require the applicant to be aged 18-30.
These types of visas allow for an initial placement of six months, with the option for the family and the au pair to extend for up to a further six months.
But there are only a limited number of countries who have reciprocal arrangements for the Working Holiday Visa or Work and Holiday Visa. As a result, most au pairs in Australia come from Germany, the Netherlands, France and Scandinavia.
"This can be broadened with the introduction of a dedicated au pair visa," Ms Kofkin said.
"We know that there are many young people from other countries who would like to take part in the au pair program, for example from Brazil."
"All nationalities should be able to apply, provided the applicant meets all the criteria."
And Ms Aylward said the current visa arrangement means "we can't track how many au pairs are in the country, nor what type of arrangements they're under".
Is there exploitation in the industry?
In a 2017 report, the Cultural Au Pair Association of Australia said it was "concerned by the lack of regulations directing the recruitment and screening of au pairs and host families".
"CAPAA members often hear horror stories from au pairs and families. Most stem from placements found through online search engines, offshore agencies or non-CAPAA agencies," it said.
"Increasingly, stories about au pairs having to work excessive hours or not being paid are appearing in the media."
SBS INSIGHT: An au pair speaks out about exploitation in a shadowy industry
The report quoted UTS's Ms Berg as saying "au pairs have very little recourse if seriously injured in the host family's home or refused promised payments by families. Equally, if an au pair leaves without notice, a family can be left in the lurch without adequate child care."
"We clearly need regulation that better safeguards the interests of both au pairs and families," she said.
As such, the Cultural Au Pair Association of Australia recommended mandatory insurance cover for the au pair, a consistent level of screening and support, and making the sponsor agency ultimately responsible for ensuring the visa regulations were adhered to during the placement.
How has the Dutton saga affected the industry?
"It's such a shame that the last week has focused at lot on au pairs visas and very little attention has been paid to what an generally enriching experience it can be," Ms Aylward said.
And Ms Kofkin said the au pair controversy has shone a light on the shortcomings of the current system.
"The au pair saga has underpinned the need for a regulated au pair program with professional support from approved agencies and a dedicated visa."
Migration agent Ms Williams said the whole episode was an indictment on Mr Dutton.
She said "in the view of the migration profession", Mr Dutton's decision "has disappointed many when there doesn't appear to have been any humanitarian grounds for him to intervene".
"It has left others whose applications are still pending disappointed and dismayed when they have a far greater need for ministerial intervention and it is in direct interests to Australian citizens," she said.