Prepare the grill for direct cooking over high heat (450° to 550°F).
In a small bowl whisk 4 tablespoons of the oil, the lime zest and juice, honey, shallot, and parsley. Season with salt and pepper.
Remove and discard the small, tough side muscle that might be left on each scallop. Lightly brush the scallops with the remaining 2 tablespoons of oil and season evenly with salt and pepper.
Brush the cooking grates clean. Grill the scallops over direct high heat, with the lid closed as much as possible, until lightly browned and just opaque in the center, 4 to 6 minutes, turning once or twice. Remove from the grill.
Whisk the vinaigrette again. In a medium bowl toss the greens with just enough of the vinaigrette to coat the leaves lightly. Arrange equal amounts of the greens and scallops on individual serving plates. Serve with the remaining vinaigrette.