What must be checked for the service brakes during the under-vehicle inspection?

During the under-vehicle inspection, it's crucial to check the service brakes for system responsiveness and leaks. This is essential because the primary function of the service brakes is to safely slow down or stop the vehicle. Checking the system's responsiveness ensures that the brakes engage properly when the driver applies pressure to the brake pedal, which is vital for safety. In addition, inspecting for leaks in the brake lines or components helps prevent brake failure, as any loss of hydraulic fluid could severely compromise braking performance and lead to dangerous driving situations.

While brake pad thickness, fluid levels, rotor condition, alignment, and tire pressure are all important aspects of overall vehicle maintenance, the specific focus on system responsiveness and leaks directly addresses the operational integrity of the brake system during the under-vehicle inspection. This makes option C the correct answer in this context.