Place grated cucumber in the center of a cheesecloth or linen kitchen towel, twist into a ball and squeeze very well until dry. Discard or save cucumber water for smoothies and soups.
In a medium bowl, add squeezed cucumber, Greek yogurt, lemon juice, olive oil, dill, garlic, salt and pepper.
Stir well with a spoon or spatula. If have time, refrigerate for 5 minutes to allow flavors develop.