When is an engine run-up recommended during de-icing operations?

An engine run-up is recommended during de-icing operations primarily to verify the proper operational status of the engine and to ensure that ice is not forming on engine components. This assessment is crucial because ice accumulation can lead to engine performance issues, potentially affecting safety. Conducting an engine run-up allows the pilot to examine the engine's response and check for abnormalities while ensuring that all systems are functioning correctly before flight.

The scenarios related to the other options do not align with the specific context of de-icing operations. Running the engine before departure for a maintenance check does not address the immediate concerns related to ice formation. Focusing on fuel efficiency does not pertain to the urgent need to confirm safe engine operation during icing conditions. Lastly, performing system checks after takeoff is not practical for addressing issues arising from ice, as such checks should occur while the aircraft is still on the ground, where any necessary actions can be taken safely.