SW updated the details for cardholders:
How will Southwest credit one standard checked bag for Rapid Rewards Credit Cardmembers and those traveling on the same reservation as the Cardmember?
All Rapid Rewards Credit Cardmembers and up to eight additional Passengers traveling on the same reservation are eligible to receive a credit for their first standard checked bag. The cost of the first standard checked bag will be refunded to the original form of payment used to purchase the bag. Customers can use any credit card for payment to qualify for the refund, including but not limited to the Rapid Rewards Credit Card. Customers do not need to call their bank to issue or receive their refund. The refund will be processed by Southwest.
Companion Pass Holders
If a Companion Pass holder qualifies for a checked baggage benefit, will the benefit apply to their designated Companion when traveling together?
Yes. If a Companion Pass holder qualifies for one or two free checked bags (based, for example, on tier status or the fare purchased), the benefit will apply to their Companion. The Companion will need to pay the applicable fee(s) at the airport, and the fee(s) will be refunded to the original form of payment.