I have never heard for a a credit card processor reporting charge backs to creditors, or charging fees.
What is a dispute fee or dispute settlement fee?
A dispute fee, or dispute settlement fee, is a fee your credit card processing company may charge you, in addition to the reversed funds, if it finds you at fault for a chargeback. Square never charges you an additional fee for a dispute. Many payment processing companies may disallow you from accepting credit cards entirely if you have an unusual amount of chargebacks on your account.
Does Square have dispute fees?
No, Square doesn’t charge any additional fees for disputes