The show’s hosts wore headbands that featured the Japanese Rising Sun flag during a martial arts inspired performance of Ciao Adios.
The flag is seen by some as a symbol of Japan’s imperialist past.
Anne-Marie also apologised for the “hurt” it had caused but said she had “nothing to do” with costumes.
ITV said it has “taken steps to re-edit” parts of Saturday’s episode for its catch-up service ITV Hub, and for future broadcasts.
The channel said any offence “was clearly unintended”.
South Korea wants the flag to be banned at the Tokyo 2020 Olympic games.
Some politicians there have compared it to the Nazi swastika.
