Passengers will not be charged a service fee if booked on the official Icelandair website.
According to Icelandair cancellation policy, there is no cancellation fee for all refundable tickets if the ticket is canceled within 24 hours.
After the flight departs, the airline will confiscate the ticket fare and there will be no refund to the passengers.

https://www.cancellation-policy.com/icelandair-cancellation-policy