2) Meanwhile, cut the fish into 1 1/4 cm cubes for the kabobs and place in a large mixing bowl. Add the tomatoes and remaining olive oil, lemon juice, lemon zest, salt, pepper, and oregano. Toss until fish and tomatoes are well coated. Add courgettes once cooled.
3) Assemble skewers and pour the remaining marinade over them. Cover with plastic wrap and refrigerate until ready to griddle. Skewers can be left to marinate for 30 minutes but no longer than 1 1/2 hours since the lemon juice will start to cook the fish.
4) Heat a griddle or griddle pan over medium-high heat. Griddle skewers and baste with remaining marinade, turning once after several minutes on the first side, until fish is just cooked through but not flaking apart, about 7 to 9 minutes total. Serve immediately.