Final answer:
A zester is the tool specifically designed for shredding the outer peel of citrus fruits, effectively removing the flavorful zest without reaching the bitter pith.
Step-by-step explanation:
A tool used to shred the outer peel of citrus fruits is known as a zester. This kitchen utensil is specifically designed to remove the zest, which is the colorful outer layer of citrus fruit skin. The zest can provide intense flavor to a variety of dishes. While a peeler can peel fruits and vegetables, a grater can shred or grate ingredients, and a masher is used to crush foods, a zester is the best tool for finely shredding the outer peel without reaching the bitter pith beneath.