GardenBanter.co.uk - Newbie question moss

We moved into an old house last summer (New England, zone 6a) and
finally have set about trying to tame the beast that is our yard. Lots
of trees, very little direct sun in the front yard (which is where the
previous owners planted many things which need direct sun - go
figure.). The owners had created about five flowerbeds, one of which
has become completely overrun with moss. Given the shade in this part
of the yard, I'm wondering if it's worth it to dig out the moss and
start over again, or if the moss would eventually creep back. (I know
that some people like gardening with moss, but I'm not one of them -
sorry, I just don't have that same aesthetic sense!)

Above this flowerbed is a gutter which was leaking - until my husband
recently cleaned it out and fixed it. I can't tell how much of the
moss problem was due to the moisture, and how much of it is from the
shade. And it's been a really, really wet spring and summer thus far
(and winter too), and we can't control that. I'm a newbie with
gardening and don't want to bite off more than I can chew with our
yard - I just want to get an idea as to whether to bother re-planting
in this garden bed, and whether I can keep moss from returning.
Thanks!