Put the syrup and mint in a small saucepan and bring to a boil. Turn off the heat and steep for about 10 minutes, then discard the sprigs and let the mint syrup cool to room temperature.
Cut enough of the watermelon into 1/2-inch cubes to measure 2 cups; set aside. Put the remaining water- melon in a blender; add the lemon juice, the rum if you’re using it, and mint syrup. Purée until liquefied. Line a fine-meshed strainer with a clean kitchen towel and set it over a large bowl; strain the watermelon purée, pressing on the pulp to squeeze as much juice out as you can. You can cover and refrigerate the soup at this point for up to several hours.
Divide the watermelon soup among 4 bowls, add the watermelon cubes and zest and garnish with mint.