The Dundalk woman is being questioned by gardaí after she arrived back in Ireland.
Gardaí are continuing to question Lisa Smith over her links to the so-called Islamic State.
The Dundalk woman left Ireland over three years ago and was deported by Turkey over the weekend along with her two-year old daughter.
The 38-year old can be held for up to three days.
Garda Commissioner Drew Harris has said a de-radicalisation programme is not needed by the gardaí for suspected terrorists.
Security and defence analyst, Mullingar's Declan Power believes the court's definition of ''membership'' will make the case of international interest:
Mr. Power outlines what gardaí will be looking out for: