But the story has a happy ending. I had received a notice from HAL that the direct seven-hour flight I'd originally booked had been changed by the airline to a one-stop flight that would take me 20 hours, with the connecting train to the airport. I called HAL Flight Ease three times and, each time, they said I'd lose the cost of the original flights if they made any change. So, today I called the airline, even though on their site it states that if flights are booked by another company then to call that company.
However, the airline, Delta, did change my flight, without any fee.