hmmm. . . . first thing i notice are the words "goldfish" in the plural sense, and "simple little tank". I'll come back to that, though.
goldfish will never win awards for being bright. they might be biting the tree to taste it, or because food gets stuck in it, or there might be a bit of algae growing on it that they like. or they could just be dumb. however, i don't think they could be biting pieces OFF of it. their functional teeth are further back in their mouths, and unless the tree is very thin or cheaply made it would be difficult for them to destroy it. i would worry more that the tree is very stiff or sharp-edged somehow, and it scrapes off a few scales every time one of them swims against it. if the goldfish are very pale or white, it could be difficult to see the missing scales. i have removed plastic plants from my goldfish tank for this reason. if it's possible for them to hurt themselves on it, they will find a way.
what size is your tank, and how many goldfish do you have in there? while the "clear plastic" definitely doesn't sound like normal fish poop, it could be descriptive of the feces from a fish with internal parasites. their poop looks white or clear-ish, like a tiny, empty sausage casing.