The display features the snowman in the image dressed in traditional republican attire.
The image at Junior McDaid House in Derry is accompanied by the phrase “they haven’t gone away ye know” - referencing the well-known Provisional IRA phrase used in the past.
The display features the snowman in the image dressed in traditional republican attire and Father Christmas appears to be holding a walkie-talkie device.
The DUP’s Foyle MLA Gary Middleton said the display was “beneath contempt” and said he has asked the PSNI to investigate.
The PSNI confirmed they are “making enquiries”.
“It is difficult to find words to describe this display in the Saoradh office window,” he said.
“To use Christmas as a propaganda tool for terrorism is beneath contempt and is an insult to victims and the wider community.
“I have asked the police to investigate, but it should be removed immediately. To show something which appears to represent a detonator being pressed is sickening, given both the current and past terrorism which blighted our city and Northern Ireland as a whole.
“There obviously needs to be condemnation of such imagery from across the community.
“However, it also needs to be accompanied by recognition that the sanitisation of terrorism and attempts to justify it in the past encourages those who engage in it today.
“The fact that dissidents are copying the same tactics and strategy of the Provisional IRA can be seen from the use of ‘they haven’t gone away you know’ emblazoned across the window.”
It is not the first instance the window has caused controversy, with similar outrage expressed back in 2019 when Father Christmas was pictured brandishing an AK-47 rifle.
In 2018 the window showed the Grinch dressed in a PSNI uniform, with a Nazi symbol on the shoulder, using a battering ram to get into a house.
In a statement PSNI Inspector Moyne said: “We have been contacted in relation to this matter and we are making enquiries.”
It comes on the same day the New IRA dissident republican group claimed responsibility for a bomb attack on a police vehicle in Strabane, Co Tyrone.
Two officers had been on patrol on Thursday of last week at Mount Carmel Heights when a bomb was detonated at the side of their vehicle.
Neither officer was injured in the attack, which caused a major security alert in the area, affecting more than 1,000 residents and leaving some children unable to get to school on Friday.