It`s up to you...you won`t hurt it either way(as long as you`re careful taking the peeling skin off!. if you remove it now, it`ll be a lot easier to clean when you`re ready to craft it. You can make some neat patterns on drying gourds by removing sections of the skin during the drying process and leaving others intact. This can give you some really neat color variations on the completed gourd. This is an example on a Mexican Bottle:
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do I just peel it off by hand...how exactly, get a little part started then peel away?:)

yep...just get a corner of the thin, outer skin and take it off like a Band-aid. Unless you take off Band-aids like my Mom used to...she`d get the Band-aid, the scab, and most of my arm off in .0000000025 seconds.