Thirteen flight attendants will fly again after United Airlines reinstated their jobs, ending a 20-month saga after the group was sacked for refusing to fly on a Hong Kong-bound plane with a “threatening” message graffitied on its auxiliary engine.

Both parties announced a resolution after the cabin crew lodged a complaint with the United States government’s Occupational Safety and Health Administration.

In July 2014, the words “Bye Bye” and two faces, one smiling and the other described as “devilish”, were found finger-drawn in oil grime under the auxiliary engine of a Boeing 747 at San Francisco International Airport.

The flight attendants, all with 18 or more years of experience, said the airline refused to deplane the passengers and conduct a security inspection. The group said they disobeyed orders to work, believing the lives of more than 300 passengers and crew on the jumbo jet could be endangered.

After a delay, the flight was eventually cancelled. United accused the flight attendants of insubordination and fired them all, according to the complaint.

We respect the right of our employees to raise concerns in good faith about the safety or security of our operations, and encourage them to do so. United Airlines senior vice-president of inflight services Sam Risoli

As a result of the settlement, announced on Tuesday, the flight attendants’ jobs have been reinstated, and they have withdrawn the OSHA filing.

“The safety of our employees and customers is paramount. We respect the right of our employees to raise concerns in good faith about the safety or security of our operations, and encourage them to do so,” said Sam Risoli, United’s senior vice-president of inflight services.

“We welcome these flight attendants back to our team,” he said.

David J. Marshall, who led the legal team representing the flight attendants before OSHA, stated that his clients were happy to have their jobs back.

“The protections that federal law provides to airline workers are essential to the safety of passenger airline operations,” Marshall said.