In a medium mixing bowl, combine the drained tuna, Greek yogurt, lemon juice, red onion, olives, capers, oregano, and black pepper.
Mix with a fork until the tuna is flaked and all ingredients are evenly distributed.
Lightly brush one side of each bread slice with olive oil.
Place two slices of bread, oil-side down, in a non-stick skillet over medium heat.
Evenly distribute the tuna mixture onto the bread slices in the skillet.
Layer the baby spinach and mozzarella slices on top of the tuna mixture.
Place the remaining bread slices on top, oil-side up.
Grill for 2 to 3 minutes per side until the bread is golden brown and the cheese has melted.
Remove from heat, cut in half, and serve immediately.