In a small pot over medium heat, dissolve the sugar in the water. Once all sugar has dissolved, remove from heat and add pomegranate seeds. Run through blender, then strain throw fine mesh strainer, keeping the liquid and discarding the solids. Chill in refrigerator until ready to use.
To make the cocktail, combine vodka, Grand Marnier, pomegranate simple syrup, and lime juice. You can shake them in a cocktail shaker with ice, or you can put them in an airtight container and store in the freezer until ready to serve (that's what I did). If you store in the freezer, just give it a good shake before adding to glass.
Serve in a martini glass and garnish with lime zest and more pomegranate seeds.