In 1-quart saucepan, heat sugar and water to boiling. Remove from heat; stir in 1/2 teaspoon lime peel and the lime juice. Cool 10 minutes.
In medium bowl, place melon and ginger. Pour sugar mixture over melon mixture. Cover; refrigerate about 1 hour to blend flavors.
Just before serving, stir strawberries into melon mixture. Serve garnished with additional lime peel.