The IRS is telling airlines that they should refund taxes to passengers who purchased tickets prior July 24th when government-mandated tariffs expired. One problem though: the airlines say that the IRS should refund the money, while the IRS says they have no way of knowing what taxes a passenger paid so they cannot refund the payments. The government agency does say, however, that they are developing a system for passengers to obtain refunds through them, rather than the airline, but there’s no timeline for getting that done.
If you purchased a ticket prior to July 24th for travel after that date, you should contact your airline and ask them to refund the taxes back to you (as they do when you purchased a refundable ticket and cancel that). You may get some pushback, but keep calling until you receive the money that is rightfully owed to you.