Delta Customers Lost Time, Money. How To File Claims, Complaints. Customers of Delta Air Lines can file claims and complaints through a number of channels if they lose money or time as a result of luggage problems, delays, or cancellations on their flights. Visit Delta's website and fill out the online claim form, supplying information and receipts for any costs incurred, to request reimbursement. Report lost or damaged luggage online or at the airport within a day of the incident. For assistance, customers can reach out to Delta's customer support by phone or social media. Formal complaints or regulatory agencies might be contacted for more assistance with persistent problems or unsatisfactory responses.