This depends on what type of sunflower you are growing. If you have the branching sunflowers such as the heleniums, then cutting back the damaged flowers to a joint or node will encourage more branches to form and you will be rewarded with more blooms. This may not work out with the giant or Pacific sunflowers that have just a single stem. In general follow a stem down to where it joins another branch and snip right above this union. May sunshine return to your garden and your rain damaged sunflowers sprout with fresh new growth. Keep growing, Marianne Binetti