What caution should be observed regarding the operation of the transfer pumps?

The correct caution regarding the operation of the transfer pumps is to avoid operating them dry. This is important because transfer pumps are typically designed to move liquid and rely on the presence of fluid to function correctly. When operated without any liquid (dry), the pumps can overheat, leading to potential mechanical failure or damage to the internal components. This not only compromises the transfer pump's functionality but could also result in costly repairs or replacements.

In the context of the other options, while there may be operational considerations involved with a full tank, the risk of damage from running a pump dry is more critical. Operating them after a flight may fall under post-flight procedures rather than a direct caution about the pumps themselves. Lastly, operating when the system is active could depend on specific system design; however, the universal caution about not running pumps dry remains paramount for safe operation.