The incident occurred in the Rathgill estate area of the city, wherein masked UDA men made threats against the young woman, telling her that she had 24 hours to leave her home or “the house is getting it.”
Mr Muir has said: “There is absolutely no place for such sinister attempts at intimidation against anyone in our community for any reason.
“It is the bare minimum that everyone deserves to feel safe in their homes. Those involved must be isolated, all they offer is fear and distress.
“We must do everything in our power to stand up to this kind of senseless intimidation, and I am engaging with the police on this serious matter.”
Cllr Harbinson added: “The behaviour displayed in the footage backing up these reports, targeting a mother with two young children, is nothing short of repugnant.
“This is not who we are in Bangor, and does not in any way represent the views of the vast majority of local people in the community.
“This is never acceptable. The perpetrators must be challenged robustly, and unequivocally, by all across society, and we will work together with police to ensure they are held to account.”