The boys were reported to Bedfordshire Police as being at risk of radicalisation in March last year but officers quickly concluded there was no issue of concern.
The school and the boys cannot be named to protect their identity as minors.
"I was told they had displayed signs that were worrying in terms of being reasonable indicators of being involved in terrorist activity. They had no other reason to believe they had any signs of extremism other than the colour of their skin," the mother, of Indian Hindu heritage, told BBC.
She claims being told that one of the boys had been speaking Arabic and talked about attending a mosque even though none of the family spoke Arabic and the children did not go to mosques.
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Central Bedfordshire Council has since accepted the children were racially discriminated against and issued an apology as well as agreed to pay an undisclosed sum in compensation.
The school's governors have reportedly found that teachers were unsure if they had a duty to report their concerns under Prevent, the UK government's anti-radicalisation strategy, which had led to this incident.
"We were called to reports of concern for safety and two officers attended - this was not in a 'Prevent' capacity but routine police attendance and the officers were only present for a short time," Bedfordshire Police said in its statement.