The correct answer is B) issue a Certificate of Discharge or make an entry in his Continuous Discharge Book. When a crew member is discharged from a towing vessel, the credentialed operator must either issue a Certificate of Discharge or make an entry in the crew member's Continuous Discharge Book. This is a requirement under U.S. Coast Guard regulations to properly document the crew member's employment history and discharge from the vessel. The other options are incorrect because: A) retaining the crew member's Certificate of Discharge onboard is not required, C) retaining the crew member's Continuous Discharge Book onboard is also not required, and D) issuing both a Certificate of Discharge and making an entry in the Continuous Discharge Book is not necessary, as either one of these actions fulfills the regulatory requirement.