DALLAS — With its flights running on a roughly normal schedule, Southwest Airlines is now turning its attention to repairing its damaged reputation after it canceled 15,000 flights around Christmas and left holiday travelers stranded.

The disruptions started with a winter storm and snowballed when Southwest’s ancient crew-scheduling technology failed. Southwest on Tuesday told customers whose flights were canceled or significantly delayed over the holidays that they would get 25,000 frequent-flyer points on top of refunds and reimbursement for unexpected costs like hotels and meals.

The airline created a page where customers can submit receipts for reimbursement; executives concede it will take many weeks to process all requests.

Danielle Zanin is still waiting to hear whether Southwest will cover the $1,995.36 that she spent during a four-day odyssey getting her family of four home to Illinois after their flight was canceled in Albuquerque, New Mexico. Even if she eventually gets the money, it may not be enough for her to try Southwest again. “It would take a lot for the airline to prove to me that they can fix whatever technology they use to get flight crews and planes where they need to go. It’s just not worth the hassle that I went through,” she said.

Raymond James airline analyst Savanthi Syth said the storm will cost Southwest about $585 million in lost revenue plus the cost of additional expenses.

Southwest remained relatively quiet for several days even after it became clear that it was struggling while other airlines recovered from the winter storm — and even after repeated criticism from consumers, media reports and Transportation Secretary Pete Buttigieg.

“The company was slow to come forward in terms of corporate PR communications until the government went after them, called the CEO directly and demanded they move fast to take care of those people,” said Larry Yu, a George Washington University professor who studies crisis management in the tourism industry. Now, he added, Southwest must make good on vows to improve its technology.

The Senate Commerce Committee said this week it will hold hearings on the Southwest meltdown. Sen. Richard Blumenthal (D-Conn.) said it was baffling why Southwest had not improved its scheduling technology after previous disruptions.

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