As mentioned, lichen. Harmless to the tree. It can indicate that the tree is not growing or shedding bark all that quickly but given the trees you’re taking about they’re not fast growers anyway.
Essentially it needs something that isn’t moving, like a rock or slow growing (or dead) branch to get established. But it wouldn’t be what caused a tree or branch to die.
Edit to add: Mary, I see what you did there and bravo.
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Noticed this green stuff all over my crape mrytle and dogwood trees this morning? Anyone know what it is? Is it harmful to the trees?