Boil water and sugar in a saucepan over medium-high heat until sugar dissolves. Cool and stir in corn syrup.
Combine balsamic vinegar, honey, and thyme sprigs in a small saucepan. Bring to a simmer over medium heat; cook 8 minutes or until liquid is thickened and reduced by half. Discard thyme; cool. Combine 3/4 cup sugar syrup, balsamic mixture, and strawberries in a blender or food processor; process until smooth. Divide mixture evenly among ice pop molds. Cover and insert craft sticks; freeze for 6 hours or until thoroughly frozen.