The court was told that Mr Burke had enjoyed certain privileges afforded to those with enhanced prisoner status such as being housed in an area with a more open regime known as "Mountjoy West".
However, his enhanced status was withdrawn after prison authorities decided his behaviour on an escorted trip to court was no longer meeting the required standard to qualify for enhanced prisoner status.
Mr Burke is challenging his transfer and has argued that moving him from Mountjoy Prison to Castlerea on 1 March has no basis in law. He has been imprisoned since January for contempt of court over his refusal to obey a court order to stay away from Wilson's Hospital School.
Mr Burke said his removal to Castlerea Prison was in breach of the order for his committal, which referred to Mountjoy Prison.
Barrister David Perry told the court the transfer of prisoners was a regular occurrence for safety or operational reasons. He said the decision to transfer a prisoner is not made by the governor but by prison service staff acting under the authority of the Minister for Justice.
He said a decision was taken to move Mr Burke to Castlerea, where he could be housed in a single cell unit. The court was told prison authorities decided there would be a risk to his safety if he was housed in the general prison population at Mountjoy, which has no single cell availability due to overcrowding.
Mr Burke addressed the court briefly this morning by video link to repeat his objections to his transfer and will make his submissions this afternoon.
The long-running legal dispute between the board of the Co Westmeath school and Mr Burke stems from incidents over a request in 2022 from the school's then-principal to address a student by a new name and pronoun.
Mr Burke, who taught German and history at the school, has repeatedly argued the direction was unconstitutional and went against his right to express his religious beliefs.
The school has been granted an injunction, restraining him from attending the school, but he has continued to attend in breach of the order, arguing that it was still his place of work.
He has been fined €225,000 and imprisoned for more than 550 days for attending the school.