Dry off the fish with a paper towel and lightly season all sides with salt.
Melt the butter in a nonstick skillet over medium high heat.
When hot, add the fish and cook for about 2 minutes until browning.
Gently flip with a spatula, reduce heat to medium, and cook the second side, approximately 3-4 minutes more until cooked through. Remove from the pan and set aside.
Meanwhile, make the grapefruit relish. Cut the top, bottom, and skin off of the grapefruit and then slice your knife right next to each segment to remove them, leaving you with just the flesh wedges (see picture).
Cut the grapefruit wedges that you have removed into chunks (a little larger than you want, as they will break some with mixing) and place in a small bowl. Squeeze the "guts" (leftover white membrane from the grapefruit) of one grapefruit into the small bowl to get some of the liquid.
Add the finely diced red onion, basil, lemon juice, and the olive oil to the grapefruit. Stir gently to combine. Season to taste with salt and pepper. If too tart, add a little sugar as desired.
Top the fish with the relish, or serve on the side. Serve immediately.