Turn off the water supply to the toilet. You can find the shutoff valve directly behind the toilet, usually near the baseboard along the wall. Turn the knob to the right to close the valve.
Flush the toilet once or twice to clear the bowl of water.
Put on rubber gloves and goggles for eye protection.
Spray a cleaning solution designed for removing rust and calcium deposits directly onto the black scratches. Allow the cleaning solution to sit on the scratches for five to 10 minutes to begin working on the stains.
Use a toilet brush or an old plastic scrubbing sponge to scrub at the black marks. If there are still visible marks, reapply the cleaning solution and allow it to sit for another five to 10 minutes. Scrub again with the toilet brush or the old plastic scrubbing sponge. Dispose of the sponge after cleaning or keep it in a special location for this type of cleaning.
Turn the water supply to the toilet back on and flush the toilet to rinse the bowl.