The moss by itself is not really a problem as it doesn't compete for nutrients the way other vigorous
weeds do.
I think it is a concern because it indicates that the soil may be too wet, too shaded or too acidic. It seems unlikely that the drainage has become suddenly worse, so I suspect the soil is too acidic.
Cutting back that tree might do the trick after a while but you might want to buy a soil test kit and see what you are dealing with. Once you know what the pH is, try to adjust it to pH 6 by adding lime in the fall.