Can you return the CARES harness? We bought a Cosco Scenera. It comes with its own bag with a carrying handle. Awesome travel seat.
You can also ask for a bag at baggage check.
We ask for bags for our stroller (can double as a luggage cart) and if the Scenera didn't already come with a bag, we'd get one for our seat as well. We ALWAYS gate check the strollers and seat. This current trip we're on, the baggage agent we pressured us to check the seat then, but we were adamant about not doing it. It's better to just buy a seat and use it on the plane tho.