I too would not worry. They are there as long as the fruit has not fully decomposed but after that they leave.
The only fruit I do not put on the heap is fruit with those fungus rings on as that is I think a soil based fungal infection and I do not want that on my beds. Everything else is fine.
And recycling is perfect.
I use the old bags as garbage bags and to transport things in so the car does not get too mucky.
