Hank here from Shopify.
There are two ways this can be done which I will detail for you below.
The fastest way this can be processed, is to have the app developer contact Shopify to provide the approval of the refund. As all app charges are third-party, they would advise of the refund, so once they contact Shopify, this would go to the billing team to approve the refund.
Then, another option is that I can reach out to the app developers on your behalf once I authenticate your store. If you want to do this option let me know, and I'll provide the next steps for you.
While both options will work, the fastest option is to ask your app developer to reach out to Shopify as you were already speaking with them, but I'm more than happy to assist you if you need this.
Let me know if you have any other questions!
All the best,
I can certainly assist with this if you prefer this option.
As this is account specific, I will just need to verify your account. I will send you an email to the email address attached to this forum's account and confirm some security questions about your store. Once you reply to that email, I will look into this further for you.