Make the syrup: Combine 1 cup of water with the sugar in a small saucepan and bring just to a boil. Set aside to cool.
Make the ice pops: Using a paring knife, cut kiwis into quarters, peel, and remove the white core and seeds from each piece. Place the seeded kiwi pieces in the bowl of a food processor fitted with a metal blade and purée to a liquid -- about 1 minute. Combine the puréed kiwi, 3/4 cup syrup, lime juice, and remaining 3/4 cup water in a large bowl. Pour the mixture into molds and freeze until solid -- about 6 hours.