Answer: Sometimes a growth inhibiting hormone (gibberellic acid) can be sprayed on the open blossoms of fruit trees to keep fruit from forming. But, with your fig tree, there's no practical way to apply growth inhibiting hormones because fig flowers form from the inside out so the spray won't reach the female parts of the flower. It may be than you'll either have to put up with the messy fruits, or you'll have to remove the fruit as it forms, but before it matures enough to ooze sticky sap. Wish there were more to suggest!
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