In a blender add the lime juice, water, triple sec, tequila, and sugar; blend until the sugar has dissolved. Set aside 8 strawberry quarters and put the remainder into the blender; blend until the strawberries are pureed. Skewer a piece of the reserved strawberries onto the end of each ice pop stick. Pour the margarita into the ice pop molds, insert the skewered sticks, and freeze at least 4 hours or overnight.
Unmold the ice pops and serve.