Zest the lime and mix the zest into Greek yogurt in a medium bowl. Mince 1 clove of garlic and add it with scallion, salt, and pepper to the yogurt. Grate the cucumber, squeeze out excess water, and fold it into the mixture. Cover and refrigerate for 15 minutes.

In a large bowl, combine olive oil, 2 minced cloves of garlic, salt, and ground pepper. Add the cleaned shrimp and lime juice. Toss to coat evenly and marinate for 10 minutes.

Heat a skillet over medium-high heat. Place the seasoned shrimp in a single layer and cook for 3-5 minutes until pink. Flip and cook another 2-3 minutes. Finish with an extra squeeze of lime juice.

Transfer the cooked shrimp to a serving platter and spoon tzatziki sauce on the side. Garnish with lime wedges or scallions and serve warm.