Lawyers for Lisa Smith, a former Irish soldier who denies membership of Islamic State, have challenged the legality of her arrest when she returned to Ireland from Syria in 2019.
Michael O'Higgins SC told the Special Criminal Court Ms Smith was arrested on suspicion of an offence under the Offences Against the State Act 1939.
He said there was no provision under that Act for offences alleged to have taken place outside of Ireland, adding that Ms Smith is charged with offences under the Criminal Justice (Terrorist Offences) Act 2005, and should not have been detained using the old act.
Sean Gillane SC, for the Director of Public Prosecutions (DPP), told the court that Detective Sergeant Gareth Kane gave evidence that when he arrested Ms Smith he suspected her of an offence of membership of an illegal organisation, which is an offence under the 1939 Act.
Mr Gillane said prosecutors, during the course of the investigation, may have later changed their suspicions, but the court must consider what the arresting garda believed at the time of the arrest.
Mr Justice Tony Hunt, presiding at the three-judge, non-jury court, will deliver a judgement on Tuesday.
Earlier, Det Sgt Kane told Mr Gillane he was aware on December 1st, 2019 that Ms Smith was on board a flight due to land in Dublin shortly after 10am.
Det Sgt Kane said he went to the airport where he spoke to Ms Smith and told her he had reasonable grounds to believe she had committed an offence of membership of an unlawful organisation.
Det Sgt Kane arrested her under the provisions of Section 30 of the Offences Against the State Act and took her to Kevin St Garda station where she was held and questioned until December 4th, at which point she was charged with an offence by another garda.
Ms Smith (39) from Dundalk, Co Louth has pleaded not guilty to membership of an unlawful terrorist group, Islamic State, between October 28th, 2015 and December 1st, 2019.
She has also pleaded not guilty to financing terrorism by sending €800 in assistance, via a Western Union money transfer, to a named man on May 6th, 2015.
Her trial continues at the three-judge, non-jury Special Criminal Court.