Originally from Palestine, the family moved to New Zealand from Syria five years ago. It was the first time they had been racially abused in this country.
The altercation lasted a matter of seconds, but left the family rattled. Saja said the incident was particularly hard after the Christchurch mosque shootings in March.
She believed her mother was targeted because of her headscarf.
"We just feel like what happened in Christchurch, it's just not fair. Losing 50 people here, and now nothing was done here.
"I just find that racist. I can't be quiet about it. We don't actually feel safe."
They were disappointed that police did not take stronger action against their abuser.
A photograph taken of the alleged attacker by the family shows a man dressed in black, in a leather jacket, and wearing glasses.
Lynnmall centre manager Caitlin Hargesheimer said mall security intervened in the altercation quickly.
Police were on site at the time, she said, and removed the man for further questioning.
Police said that after speaking to both parties and watching CCTV footage, they gave the man a formal warning.
The Human Rights Commission said it had received 295 complaints in the last five years which it categorised as anti-Islamic, though it could not say with certainty whether such incidents were becoming more common.
The complaints ranged from a student being called a "terrorist" by fellow students to women being barred from shops because they were wearing a hijab.
The commission's figures did not cover the period after the attacks in Christchurch.
