Sakina Dharas, 24, her sister Maryam, 19, and their brother Ali, 21, were on board EasyJet flight EZY3249 from London's Stansted Airport to the Italian city of Naples on August 17, aljazeera.com reported.
As the plane was about to take off, a crew member ordered the siblings off the aircraft and escorted them down the staircase to the tarmac, where they were met by armed police and an MI5 agent who questioned them for one hour, Sakina was quoted as saying.
Two passengers told authorities that the siblings had been looking at a mobile phone screen that showed either Arabic text or the words "praise be to Allah", Sakina said.
"A passenger on your flight has claimed that you three are members of ISIS," the MI5 agent said to the siblings, according to Sakina.
"The minute that I saw police standing there, I was extremely emotional. We had nothing at all [on our phones]. We don't even speak Arabic, we're [of] Indian [origin]," she said.
During their one-hour interrogation on the tarmac, Sakina said she was asked to explain - page by page - the details of various entry stamps on her passport. She also showed the MI5 agent recent WhatsApp messages.
The siblings provided answers relating to their personal lives and were questioned on their home addresses, workplaces, social media history and parents' professions.
The siblings, from northwest London were then allowed back on the plane, which had been delayed.
Sakina said she and her siblings were victims of "racial profiling".
"I'm still very annoyed that someone [the accusing passengers] can get away with a blatant lie," she said, adding that she would take legal action "if I knew a way to do so".
The airline has now apologised after the incident at Stansted last week as the three were heading to Naples for a weekend getaway.
"We would like to apologise for any inconvenience caused to the passengers," the company said.
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