In a small bowl, combine the mayonnaise, ketchup and relish. Season to taste with salt and pepper. Set aside. (I find that it's easiest to put this on the hot dogs when I put it in a small ziptop bag and cut the corner off.)

Heat a grill or griddle over medium-high heat. Wrap each of the hot dogs in a slice of pastrami. Place on the grill, seam side down, and cook until the hot dog is warmed through and the pastrami is lightly crisped. Add a slice of cheese to the top of each, cover, and cook another minute or two until the cheese has melted. Transfer the hot dogs to the buns.

Top each hot dog with some of the sauerkraut, then drizzle the dressing on top.