A Stripe account is needed so that Returnly can send money to your account to settle repurchases. Stripe is our method for exposing our credit facility and allowing us to pay you for repurchases (through Returnly Credit) as well as exchanges.
These transactions are fronted by Returnly, and Returnly assumes the fraud risk. You (as the merchant) will not be responsible for any fees related to processing Stripe transactions, since Returnly assumes these costs.
Additionally, this connection to Stripe is irrelevant to your existing payment processing system - so nothing will change with how you receive or refund payments to your shoppers.