Answer: Moss grows where soil is shady, moist, acidic, and compacted. Under your Japanese maples sounds like a perfect growing spot for moss. I think it adds a bit of character to have moss growing under Japanese maples but if you don't like it, carefully scrape it off the top of the soil (so you won't harm the roots of the maple). You can break the soil surface up a bit to help loosen the soil so moss won't be so prone to grow there.
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