Thanks! It's a good question and I haven't given it too much thought yet. For now I am just handling all disputes myself, if they get overwhelming I'll have to automate some aspects of it. It'll be interesting finding the balance between making it easy to get a refund when it's necessary but not so easy that the users would want to dispute it on regular basis.
Happy to answer such questions! By disputes I believe @hackandtrip means customers disputing charges with their credit card company. Aka chargebacks.
Beeminder gets zero credit card disputes because we give people a chance to contest their derailments and cancel the charge before it goes through. They have to talk to a human workerbee but we make it as easy as possible. If that doesn't happen in time and the charge goes through but the user still doesn't think it was legit for whatever reason, we refund it. No need for it to ever get disputed with the credit card company.
Love the fact that you make it easier for the customer to get a refund through your process, than through the refund one; I do not work in this space and offering free refunds for my product could be very destructive, but it makes 100% sense here.