Preheat an outdoor grill for high heat and lightly oil grate.
Cut a slit in steak to create a pocket that is open on one side only. Mix together 1 tablespoon olive oil and lemon juice in a small bowl until well combined; brush over both sides of fish. Set aside.
Heat 1 teaspoon olive oil and garlic in a small skillet over medium heat. Cook spinach in hot oil and garlic until wilted. Remove from heat and stuff into pocket. Place feta in pocket over spinach.
Cook fish on the preheated grill for 8 minutes. Turn over and continue cooking until cooked through. An instant-read thermometer inserted into fish should read 145 degrees F (63 degrees C)
