Transfer the cucumber to a mesh strainer to drain the excess liquid and sprinkle with a ¼ teaspoon of salt (to help draw out the liquid). Using your hands, press out the excess water and squeeze it as dry as possible.
In a medium-sized mixing bowl, combine the garlic, olive oil, and lemon juice. Stir to combine.
Add the Greek Yogurt, and stir into the garlic mixture. Finally, stir in the drained and grated cucumber. Season with salt and white pepper to taste.
Tightly wrap the bowl in plastic wrap and refrigerate for 2 hours before serving. Store in an airtight container in the fridge for up to 3 days.