Ireland agreed to repatriate Lisa Smith, 38, and her two-year-old daughter after Ankara began deporting foreign citizens linked to Islamic State earlier this month.
Turkey says it has captured 287 militants in northeast Syria, where Turkish troops launched an offensive against the Kurdish YPG militia last month, and has hundreds more jihadist suspects in detention.
Dublin has said for months that it has a responsibility to bring Smith back to Ireland and that its main concern was for the safe repatriation of her daughter.
The girl was now being cared for by relatives, police said.