The north's chief electoral officer has indicated flags will only be removed from polling stations if considered "excessive".
Sarah Ling was speaking after a picture was circulated claiming to show a polling station at Blythefield Primary School in Belfast's Sandy Row area bedecked in union flag bunting.
Ms Ling told The Irish News she only learned about the image after the election.
She declined to say whether she regarded the bunting display as excessive.
The school in question, situated in the Botanic DEA, has directed all media queries to the Education Authority, which has yet to comment.
Earlier this month, Blythefield PS won a competition to design a bench to mark King Charles III's Coronation.
Tasked with designing a bench to mark the occasion, children from the school drew crowns, an orb, a sceptre and stags for the bench, which was brought to life by an artist and is on display at Royal Hillsborough.
SDLP councillor Gary McKeown said he was contacted by a constituent concerned at the display as they cast their vote.
"It wasn't until I saw the photograph that I realised how bad it appeared to be," Mr McKeown told The Irish News.
"It is essential that all steps are taken to ensure that polling stations in any area are politically neutral and welcoming to voters.
"The smooth and fair operation of the electoral process is at heart of our democracy, so anything that could put people off voting or make them feel uncomfortable is completely unacceptable."
He added: "If it is verified that this image was taken at that polling station, I fail to understand how anyone thought that this was appropriate, and why steps weren't taken to fix it."
The image was described by one Twitter user as a "unionist gauntlet" that voters were forced to walk, while GAA pundit Joe Brolly shared it with the caption "Welcome to Northern Ireland".
Fermanagh and Omagh UUP councillor Victor Warrington, who was re-elected on Friday, replied to Mr Brolly's post, stating: "It is our national flag."
A statement from the Electoral Office said: "In general in the use of primary school facilities we take the space as it is used by the school and we do not remove materials but rather provide space for our tables, booths and boxes.
"It is acceptable to have a flags (sic) on the wall of a primary school and this office does not have any authority to interfere in the material displayed within the school when we use the facility as a polling station. However, if the display is excessive, we may discuss with the school about minimising such display. We were not aware of this issue on polling day.’"