Clean and spray grill grates with non-stick cooking spray and set heat to high. Close the lid and allow the grill to come to temperature.
While the grill heats, prepare the gremolata by combining the parsley, lemon zest, preserved lemon rind, and garlic in a small bowl. Season with salt and black pepper to taste and set aside.
Brush tuna steaks with olive oil and season with Mediterranean-spiced sea salt and black pepper on both sides.
Open the grill and place the tuna steaks and lemon halves over direct heat. Do not close the lid. Cook for 2 minutes per side for rare, or slightly longer for medium. Do not overcook.
Remove from the grill and serve immediately, topped with gremolata and with grilled lemon halves alongside for squeezing.