Combine the sugar, water, and corn syrup in medium saucepan and cook over medium heat for about 5 minutes, until all the sugar is dissolved. Once the sugar just comes to a boil, lower to simmer and add the tea bags. Continue to cook on low for 5 minutes. Turn off heat and let steep for at least 30 minutes or longer. When cool, pour into a storage container or squeeze bottle and refrigerate until ready to use.