People often buy “organic” fruit on the supposition that pesticides are not used during its growth. Quite apart from the fact that the term “organic” means precisely nothing, the presence or absence of pesticides during growth of the fruit is utterly inconsequential.
This is not the case in all parts of the world, but it is most certainly the case in Australia, which places very strict controls on the type and amount of chemicals that may be used on crops. This is administered by a federal authority called the APVMA (Australian Pesticides and Veterinary Medicines Authority).
This organisation is extremely conservative in both the pesticides that it allows growers to use, and the amounts that they can use. Their permits are based upon both medical data and testing of fruit that has been sprayed under various conditions. In fact the limits they impose are so conservative that they have caused a great deal of disquiet amongst growers, who feel that they are unnecessarily restrictive in terms of the limits that they set.
But the upshot of this from the consumer point of view is that you may rest assured that the fruit on the shelves in your supermarket has nowhere near any levels of pesticides that could even come close to doing you any harm whatsoever. And note that these restrictions apply to not only the amounts that can be sprayed, but the actual choice of insecticide in the first place, with several insecticides that have been successfully used for years having now been banned.
So in effect there is no insecticide on any fruit that you buy. You may still wish to wash it, perhaps to wash bacteria off the surface from having been handled, but you don’t need to worry about pesticides.