Final answer:
The liability for the damage done to a vessel while under the control of a pilotage and towing firm falls on the insurer of the firm.
Step-by-step explanation:
When a pilotage and towing firm is responsible for damage done to a vessel while the vessel is under its control, the liability for the damage would typically fall on the insurer of the pilotage and towing firm (option 4). The pilotage and towing firm usually carries insurance coverage to protect against such damages. Therefore, the insurer of the pilotage and towing firm would be liable for the damage.