Some of the Irish tourists accused of defrauding residents and stealing from businesses and elderly residents across south-east Queensland have fled the country, police say.

Since January, the group of men and women have been linked to 12 incidents across Brisbane and the Gold Coast, scamming people out of thousands of dollars in a scheme police described as "seamless".

The women allegedly focused on shops and restaurants, while the men seemed to single out homeowners by taking payments for house repairs but failing to follow through with the work.

In one case, an elderly man lost more than $25,000 when he paid men to repair his roof, but they never finished the job.

On Monday afternoon, Detective Superintendent Tony Fleming said most of the group left the country from Sydney after their images were released on Saturday.

"They've drawn a lot of attention to themselves, and certainly caused some havoc across parts of south-east Queensland," he said

He said there had been no additional reports of further crime.

Police allege these two men are part of the scam, claiming to have found hair in their food at a Brisbane restaurant and then leaving without paying ( Supplied: Queensland Police Service )

"I think it's reasonable to assume that's as a result of great attention both on social media and general media by the release of the photographs of these people, and bringing it to the attention of everyone," Superintendent Fleming said.

He said four people from the group remained in the country — two men and two women.

Police want to speak to this woman. ( Supplied: Queensland Police Service )

Superintendent Fleming said police were working closely with the Australian Border Force to monitor the activity of the four remaining suspects.

"We've given them an alert, and said if those people come through to you ... let us know and then we'll make an assessment on what we're going to do," he said.

"It depends when, it depends where, and I'm not trying to be ambiguous, but it may well be best that we let them leave the country."

Superintendent Fleming said more than 20 people, including children, who were linked to the fraudulent activity had left the country, but not all were suspects.

"My understanding is they took a number of flights and they've probably headed off into Asia," he said.

He said police would need to consider the costs associated with extradition against the likelihood of conviction and restitution for victims.

"I really hate to be talking about dollars when we're talking about justice, but there is a balancing act there, about making sure our community's safe to prevent more offences, versus what is the likely outcome of this," he said.

Superintendent Fleming said as for the group of tourists already out of the country, police would do their best to make sure they couldn't cause more damage.

"Wherever it is lawful we will continue to share information with Border Force, who also have arrangements with their partner agencies around the world, and we will certainly do everything we can legally to make it difficult for them to enter into any country to commit those offences," he said.

"It's pretty obvious to us based on some of our findings so far that this attention has put many of them to ground, which is a good thing because our key goal at the moment is to stop these people committing any more offences."

He said those remaining were being investigated over allegations of fraud and property damage.

An Australian Border Force (ABF) spokesman confirmed "a number of the group have now departed Australia voluntarily".

"We are working closely with Queensland police regarding those remaining onshore, and also engaging with international partners to ensure all relevant information on the group is understood and shared," he said.