There is green moss growing on the branches of my Japanese Maple. Will this hurt the tree? How do I get rid of it? Can I just leave it alone?
It indicates the tree is growing slowly plus you have good air quality in your region plus the prevailing climate/weather provides adequate moisture.
So, it's not a problem.
Abundance of mosses on other trees and shrubs under suitable climate and site conditions (damp) indicates specimen does not have to be growing slowly.
Lichens have been thought to accumulate on slow-growing shrubs. Those are not "green moss".
And, as with mosses lichens are so abundant on some sites I have to wonder if there really is a consistent association with slow growth in that case also.
You can get rid of it by scraping it off.
Some will say not to bother while others do advocate removing it if you can reach it.