Light a grill. In a large bowl, combine the lime zest and juice with the 1 tablespoon of olive oil. Using a rubber spatula, gently fold in the diced honeydew melon and avocado. Season the salsa with salt and black pepper.
Drizzle the scallops with olive oil and season with salt and black pepper. Grill over moderately high heat, turning once, until nicely charred and just cooked through, 3 to 4 minutes per side. Transfer the scallops to plates, spoon the salsa alongside and serve.