Grate the cucumber onto a double stack of paper towels. Fold the towels around the cucumber. Over the sink, squeeze out as much excess water as possible, adding another layer of paper towels as needed.
Transfer to a bowl, then stir together with the Greek yogurt, garlic, lemon juice, dill, olive oil, and salt. If time allows, cover and refrigerate for at least 30 minutes or up to 3 days (or use it right away and know the leftovers will taste even better!).
Notes
TO STORE: Refrigerate in an airtight container for up to 3 days. Give it a good stir before using it.