Mix the yogurt with 1/4 teaspoon of salt. Spoon the yogurt into a cheesecloth-lined strainer set over a bowl and let drain for 2 hours.
In a bowl, mash the yogurt with the feta until smooth. Add the garlic, cayenne, paprika, 1 tablespoon of the olive oil, and black pepper and mix well. Alternatively, puree in a food processor or blender.
To serve, spread the cheese on a serving plate. Drizzle with the remaining 1 tablespoon of olive oil and garnish with olives. Serve with warm pita bread.
The cheese dip can be prepared 24 hours in advance and refrigerated. Bring to room temperature before serving.