The three siblings said that they were made victims of racial profiling and demanded an apology
Three women were asked to deplane and questioned on the tarmac by police officers over allegations that they were Islamic State supporters.
The three siblings - Maryam Dharas, 19, Sakina Dharas, 24, and Ali Dharas, 21 - had boarded the flight from Stansted to Naples.
The women, residents of north-west London, were interrogated for an hour by the police.
Maryam later said that they were subjected to racial profiling.
Before letting them go, Sakina was told that further background checks would be conducted.
Maryam also said that she needed an apology.
The airline insisted that security concerns had to be investigated, while the police offered no apology.
The Dharas siblings, who are of Indian ethnic origin, were asked if they had Arabic text on their phones or copies of the Quran.
A couple on the plane had reported that the sister were reading some Islamic State material on their phones.
Sakina had a passport stamp from a visit to Iraq, where she had participated in a walk to raise funds for IS victims.
The officers also asked Maryam to show her Twitter posts.