birds have a sixth sense ability to spot mangoes that are 2 days away from ripening, regardless of whether they're totally green or hidden under a bunch of foliage. It's like mango ripening radar that God gave them.
However, I absolutely adore the birds in my yard and gratefully accept pecked mangoes in exchange for their graceful singing and peaceful beauty that they bring.
You can eliminate the nest in your tree, but it's totally moot, since they can quite easily spot your fruits from miles away. And there are millions of them in florida. It's like trying to hide from the NSA. good luck.
:-)