It wasn't until the next day that I took a closer look, and found that they were strips of bark, like a beaver leaves around the base of a tree it's been gnawing on. This was surprising, since there are plenty of trees I'd think wd be more appealing, not to say handier, lining the little stream that runs nearby, and a solid wooden fence some six feet high separating the path by the stream from this particular tree.
Checking more closely, I found the strips weren't from the base of the tree but higher up, some twenty or thirty feet from the ground, where I could see that a major limb was losing its bark on its top side. It can't have been struck by lightning, since its leaves are still green and unwithered. I can't think of any bird that could strip bark like that. Deer can't reach that high, and anyway wouldn't eat bark when there was fresh green grass growing all around, even if we had deer in our neighborhood, which we don't. Giraffes are right out.
So, thinking it over, I've come up with an explanation I'm going to use until I find out what really happened:
It fits the known facts, and passes the truthiness test. Now all I need is some evidence (that is, some other evidence), that tree beavers exist. In these days of Climate-Change deniers,* Creationists, and what-not, how hard can it be?