An Australian television crew accused of aiding a mother in the botched kidnapping of her two children in Lebanon flew home Thursday amid reports of a multi-million dollar deal struck with the father to drop abduction charges.

Brisbane mother Sally Faulkner and the Channel Nine team were arrested and charged last week after Faulkner's son and daughter were snatched in broad daylight on a Beirut street.

But they were released on bail Wednesday after the father, Ali al-Amin, decided not to pursue the charges in court.

Faulkner's lawyer Ghassan Mughabghab said a deal had been struck granting Amin full custody of the children in line with Lebanese law.

The commercial Nine network did not mention any deal they were reportedly behind, but announced a full inquiry into the bizarre episode.

The Australian newspaper said ‘a multi-million dollar deal was struck to drop abduction charges’.

‘Nine pays dad to win freedom for crew and mum,’ Sydney's Daily Telegraph headlined, adding that ‘a massive sum of cash’ had been paid in compensation.

The Sydney Morning Herald said it had cost several hundred thousand dollars, but that an exact figure could not be confirmed.

- Planned boat escape -

The crew and Faulkner still face potential charges by Lebanon's public prosecutor, but they can be sentenced in absentia.

Amin's lawyer Hussein Berjawi told AFP he has not dropped charges against two Britons and two Lebanese allegedly involved in the abduction through a child recovery agency.

Faulkner however remains in Beirut for a custody hearing with her estranged husband.

Bailed star reporter Tara Brown led her producer, cameramen and sound recordist on to the earliest flight out of Beirut after their release from custody.

The Nine team were due to arrive in Sydney Thursday night.

It was a disastrous end to the news story they had planned.

‘They intended to get away in a boat captained by a member of a private child recovery agency,’ a Lebanese security source said.

The crew were arrested April 7, a day after her children were grabbed.

Video shows them walking with an elderly person said to be their grandmother before several figures jump out of a car, shove the adult aside and carry the children off in the vehicle.

Police later found Faulkner with the children, reportedly a six-year-old girl and a four-year-old boy, at a home in Beirut. They were handed back to their father through the courts.

Faulkner accused him of taking them for a holiday to Beirut and then refusing to return them to Australia.

The channel's handling of the coverage has proved controversial in Australia and Prime Minister Malcolm Turnbull issued a warning.

‘We are very pleased they (the television crew) are on their way home,’ he said, ‘and we want to thank the Lebanese authorities for their cooperation’.

But he added: ‘All Australians, regardless of what they do or who they work for, should recognise that when they are outside of Australia, they must obey the laws of the country in which they are visiting.’

Nine Network chief executive Hugh Marks pledged to ‘ascertain what went wrong and why our systems, designed to protect staff, failed to do so in this case’.

‘What has happened to Sally happens all too often and affects thousands of Australian families,’ he said.

‘It is a story that not only is profoundly in the public interest but also one the public is interested in.’