Preheat the grill to medium-high and brush the grate with oil or spray with nonstick cooking spray.
In a large bowl, fold together the crabmeat, bell pepper, mayonnaise, mustard, Old Bay seasoning, lemon zest, black pepper, scallions and celery. Sandwich about 1/4 cup crab mixture between 2 slices of the bread. Repeat with the remaining crab mixture and bread slices. Brush both sides of each sandwich with olive oil.
Transfer the sandwiches to the grill. Close the cover and cook, turning once, until both sides are golden and lightly charred, about 1 minute per side.