Yes, you can easily issue a refund.
When you collect a payment through Stripe, you can issue the refund directly from the payment page in the system. This will actually refund the funds to the client.
Payments collected via the system through PayPal and refunded through the system, will be "Marked as refunded". You will be able to issue the actual refund directly from your PayPal account.
Other payments that were "Marked as paid" could be "Marked as refunded".