The airline confirmed news reports from passengers it had sent the cheques along with $1,000 travel vouchers. "We can confirm the communication and gesture are authentic and heartfelt," the company said in a brief statement on Friday.
The CFM56 jet engine on Southwest flight 1380 blew apart over Pennsylvania on Tuesday, about 20 minutes after the Dallas-bound flight left New York's LaGuardia Airport with 149 people on board. The engine debris shattered a window on the Boeing 737 plane, killing a passenger - the first death in a US airline accident since 2009. The plane made an emergency landing in Philadelphia.
The Federal Aviation Administration said late on Wednesday it was working to quickly finalise an airworthiness directive within the next two weeks that had been proposed in August 2017 after a similar engine failure in a Southwest plane in 2016, which it said would apply to 220 engines.
National Transportation Safety Board investigators on the scene were expected to wrap up their work in Philadelphia on Saturday, the agency said on Friday.
Southwest said after the incident that it was accelerating its existing engine inspection programme "out of an abundance of caution" and expected to complete it over the next 30 days.
The FAA order will require ultrasonic inspection within the next six months of the fan blades on all CFM56-7B engines that have accrued a certain number of takeoffs. Others more recently serviced will require inspections within 18 months, the FAA draft order said.
Airlines told the FAA last year that because fan blades may have been repaired and moved to other engines, the order would affect far more than 220 CFM56-7Bs, which are made by a partnership of France's Safran SA and General Electric Co.