Dampen a paper towel in white vinegar. Depending on the amount and location of the limescale, soak more than one paper towel or cut the single paper towel into multiple smaller sections.
Lay the paper towel over each area of calcification. For the faucet mouth, wrap a rubber band around the paper towel to keep it in place.
Allow each paper towel to remain for at least one hour. Remove the paper towels afterward and discard.
Dust the affected area on the faucet with baking soda. Dampen a plastic mesh scrubber with water and scrub each area clean.
Turn the aerator housing counterclockwise by hand. If the housing proves difficult or is impossible to turn, wrap electrical tape around the jaws of some pliers. The tape pads the pliers, preventing any damage to the aerator housing. Use the pliers to remove the housing.
Place a hand directly beneath the aerator housing to catch the housing as it falls. Set the housing aside for the moment.
Pour enough white vinegar into a bowl to fully submerge each of the aerator parts.
Disassemble the aerator inside the housing carefully. Remember to reassemble the parts in the correct order.
Submerge each part in the vinegar. Allow the parts to remain in the vinegar for one hour.
Remove the parts from the vinegar. Observe whether any sediment or calcification remains on the aerator screen. If so, straighten a paper clip and use it to clear any clogged holes in the screen.
Reassemble the aerator. Thread the housing back into the faucet nozzle and tighten.