@qwilliamson Have you used the pay-by-refund feature? The bank, Santa Barbara Tax Payer Group, will issue Prepaid cash Green Dot cards for refunds. TPG Bank bank will have account and routing information of its own for your participating clients, it's not the routing and account number of your clients regular bank. This is what I know about Green Dot, other than that you may want to reach out to support for more details on this topic. I hope this helps. 

Screenshot from the pay-by-refund page linked above..."Learn more about participating banks":