Boil 1/2 cup water + dissolve the sugar stirring slowly to make the simple syrup. Set aside and let cool. In a blender add your honeydew and about 1 tsp of the simple syrup and pulse until it's a liquid consistency - you might need to add some more simple syrup so it can blend properly.
Using a muddler or wooden spoon mash the strawberries and mint leaves in the bottom of your pitcher, add the liquefied honeydew. Add in the lime juice and rum and 1/4 cup of simple syrup {can add more if you want it sweeter taste test it first}.
Right before serving pour in the club soda.Gently stir to combine and pour over iced glasses and garnish with fresh mint sprigs, lime and strawberries if you'd like.