Nobody else has suggested the credit card dispute route (since
@Patina) and that is what I was also thinking. Isn't that the simplest way to resolve this or is there a reason that can't be done.
You bought the tickets in January 2020. Generally, a credit card dispute must be filed within 60 days of the date of the bill on which the charge appears. That deadline would have passed in March 2020, or thereabouts.
There is an argument that a failure to post a credit or return regarding an old transaction can also be used to re-set the clock on a billing error dispute. In your case, you do not have a receipt showing a refund, and it does not appear you know the amount of the refund. However, you can certainly call your bank and ask whether they would accept a failure to post the promised refund in this instance would be treated as a billing error. While I think your chance of success is low, it just requires the investment of a small amount of time. The statute provides that a billing error includes:
(4) The
creditor’s failure to reflect properly on a statement a payment made by the obligor or a credit issued to the obligor.
(You are the obligor here.)
Banks in this situation won't stand up for their customers, because the bank might have to pay the refund amount out of its own pocket, if GoToGate is out of funds.
In better times, we pursued such an out-of-time credit card dispute with Citibank regarding a vendor often mention on this site. We lost both the credit card dispute and travel insurance claim. Frankly, I can't say Citibank was wrong, so don't take this as a ding at Citibank.
You can find a full discussion of your rights under the Fair Credit Billing Act at:
Here’s how to resolve billing errors on your credit card accounts.
www.consumer.ftc.gov