Agile doesn't help you here. It might only take a day to fix this issue in your code base. But then it will take months to get it tested and approved. And then

Agile doesn't help you here. It might only take a day to fix this issue in your code base. But then it will take months to get it tested and approved. And then it has to be rolled out into the organization and periodically analyzed during the rollout until it's done. Given how large airlines are and how many people interface with an airline booking system Agile's "contribution" to development timing is meaningless here. You could spend a day making a fix and a couple years watching that fix slowly percolate into the organization, followed by another couple of years waiting for all the travel agents to stop calling and complaining about how this impacts the workflow they've had for the last 20 years.