The offer comes after Southwest announced last week that it would end its long-standing two-free checked bags policy for most passengers. The move is one of several major changes at the airline, from the addition of premium seating to seat assignments, and prompted pushback from some loyal flyers.

Frontier Airlines took a dig at Southwest by offering newer amenities for travelers as it ushered in its so-called "New Frontier."

Budget carrier Frontier Airlines is offering free checked luggage and economy bundles that come with seat assignments and carry-on bags.