Add the potatoes to a medium saucepan with enough cold water to cover by at least 2 inches. Set the saucepan over medium heat. Bring the water to a boil and continue boiling until the potatoes are tender, about 15 to 20 minutes. Drain the potatoes in a colander and allow them to dry for 5 minutes.
In a serving bowl, add the potatoes, tomatoes, scallions, olives, parsley, capers, thyme, olive oil, and lemon zest. Toss gently until all the ingredients are coated and season with salt and pepper, to taste. Refrigerate for 1 hour and gently toss again before serving.