I haven't grilled branzino filets (I always grill it whole) but the skin should release once it's cooked. A good tip I learned when I learned how to grill a whole fish -- best way to tell if it's ready to flip is whether the skin releases with minimal effort or if it sticks, if it sticks it needs more time. That tip applies to more than just fish too).

For the whole branzino, I typically stuff it with lemon and herbs (typically rosemary), I would think you could do something similar with a filet