Heat a grill set up for direct grilling until hot; brush the grill rack with oil.

Puree the salsa until smooth in a blender or food processor.

Boil the wine in a medium skillet over high heat until reduced by half. Add the salsa and heat to boiling. Reduce the heat to a simmer; stir in the butter until melted and incorporated into the sauce. Season with salt and pepper and keep warm.

Remove any short, hard strips from the short edge of the scallops. Pat the scallops dry with paper towels, and season with salt and pepper.

Coat with oil and grill until the scallops are resilient and browned on both sides, about 2 minutes per side.