The process of removing all of the old brake fluid from the hydraulic system is called

Flushing is the process of completely removing the old brake fluid from the hydraulic braking system and replacing it with fresh brake fluid.

Brake fluid can absorb moisture and contaminants over time, which may reduce braking efficiency and cause corrosion inside the brake components.

Bleeding is different because it mainly refers to removing trapped air bubbles from the brake lines, not completely replacing all the fluid.

Therefore, the correct answer is Flushing.