Lisa Smith is expected to be questioned by Gardaí for two more days surrounding her activities with the so-called Islamic State.
The Dundalk woman was arrested yesterday after being deported from Turkey.
The 38-year-old left Ireland over three years ago and was taken back yesterday along with her two-year-old daughter who is being cared for by relatives.
The Government say the young child has been their primary concern.
It's reported in the Irish Independent that Ms. Smith is keen to give her side of the story to investigators.
"Lisa Smith at the moment is innocent until she's proved otherwise," said Independent Senator Gerard Craughwell.
"She is a citizen of the State. We can all criticise her for taking off to join ISIS.
"I would be the first to say as a former member of the Defence Forces, she knew exactly the people she was going to join up with. She's going to have to explain all of that."
The Dundalk woman was taken into Garda custody after the Turkish Airlines flight she was traveling on landed Dublin Airport.
She will be questioned again today at Kevin Street Garda Station in Dublin on suspicion of terror offences and can be held for up to three days.
The Irish Times say her likely defence to charges will surround the definition of the word "membership".
Meanwhile, there are still question marks surrounding what will happen to the Dundalk woman after being questioned. It is reported today she could face up to seven years behind bars for her association with a terrorist organisation.
"She represents Dundalk unfortunately on the public forum," said the editor of the Dundalk Democrat David Lynch. "I think people in Dundalk are aware of that. There are sympathies for her daughter - but there is the understanding that Lisa Smith needs to be questioned thoroughly."
