Using a vegetable peeler, peel outer skin and tough green layer from watermelon rind; cut rind into 2-by- 1/2-inch strips.
In a medium saucepan, combine 5 cups water with 3 tablespoons salt; bring to a boil. Add rind. Cook at a rapid simmer over medium-high until crisp-tender, about 5 minutes. Drain, and transfer to a heatproof bowl (reserve saucepan).
In reserved saucepan, combine vinegar, sugar, pickling spice, remaining teaspoon salt, and 1 cup water. Bring to a boil, stirring to dissolve sugar and salt; pour hot liquid into bowl with rind. Use a small plate to submerge rind into liquid. Let cool to room temperature. Transfer to a container; cover and refrigerate in liquid at least 2 hours and up to 2 weeks.