Place grated cucumber in a sieve over a bowl and sprinkle with salt. Let sit for 10 minutes to drain excess moisture.
In a mixing bowl, combine Greek yogurt, minced garlic, olive oil, lemon juice, chopped dill, salt, and pepper.
Squeeze out any remaining liquid from the grated cucumber and add it to the yogurt mixture. Stir well to combine.
Taste and adjust seasoning as needed.
Refrigerate for at least 1 hour before serving to allow flavors to meld.
Serve chilled with pita bread or as a sauce for gyros or grilled meats.