Details transferring a domain AWAY from AWS

Typically, no costs are involved when transferring a domain from Route 53 to another registrar. However, the new registrar may charge a fee for the transfer.

The AWS documentation is unclear, but you will notice that it does not mention cost. https://docs.aws.amazon.com/Route53/latest/DeveloperGuide/domain-transfer-from-route-53.html

The case of transferring to Route53 explains the transfer cost if there is a cost involved. https://docs.aws.amazon.com/Route53/latest/DeveloperGuide/domain-transfer-to-route-53.html