Including white pith while zesting will make your dish taste bitter because the pith contains compounds called limonoids, which are naturally bitter.
The zest of citrus fruits, like lemons, oranges, and limes, is the colorful outer layer of the peel. This layer contains aromatic oils that add a bright, citrusy flavor to your recipes. Beneath the zest lies the pith, the white, spongy layer between the zest and the fruit's flesh. The pith is composed of different compounds than the zest, most notably limonoids. Limonoids are a class of chemical compounds that are known for their intensely bitter taste. When you zest a citrus fruit, you want to remove only the colored outer layer, avoiding the pith. If you accidentally include some of the pith, the limonoids will leach into your dish, imparting a bitter flavor that can overwhelm the other flavors. The amount of bitterness will depend on how much pith you include. A small amount might be barely noticeable, while a larger amount can make the dish unpalatable.
Use a microplane zester for best results. Its fine blades make it easier to remove just the zest without digging into the pith. Apply gentle pressure and stop as soon as you see white.