A few questions...does the stuff rub off? Is it powdery? Is it ON the limb or IN the limb?

It kind of rubbed off. Not powdery. I actually think I solved the mystery though. I remembered that my husband had applied some clear gel bird repellent in that tree maybe a year ago where birds would sit and leave droppings all over the patio and grill. I showed him these spots and he said that was right where he'd applied the repellent. So I think that's what it is. Mystery solved. (I think).

Good for you..next time you might want to try bird scare. Comes on a roll like masking tape, looks like xmas tinsel just tie it on. We use it on the fruit trees and grapes