In a medium bowl, combine the grapefruit and all but 2 tablespoons of the juice, the scallions, jalapeno and 2 tablespoons olive oil; season with salt and pepper.
Preheat an outdoor grill or a grill pan to medium-high. In a medium bowl, toss the fennel with 1 tablespoon of the olive oil and the remaining 2 tablespoons grapefruit juice; season with salt and pepper.
Arrange the bread slices on a work surface; top each with a slice of cheese, one-quarter of the fennel, one-quarter of the arugula and a second slice of cheese. Cover with the remaining bread slices.
Brush one side of the sandwiches with olive oil. Place oil side down on the grill; brush the tops with olive oil. Grill, turning once, until the cheese is melted and grill marks appear, about 7 minutes. Serve with the spicy grapefruit salad.