Crows have a lot of interesting behaviors, but in this case, we strongly suspect one or more squirrels. They may use the strips (the ones they didn't drop, anyway) to augment their nests, or just to have something to gnaw (as rodent teeth are ever-growing and need to be worn-down), or to access the mineral-rich sapwood that lies just below the bark. There unfortunately isn't a reliable way to deter them, though the tree can probably recover by gradually sealing-over the injuries on its own, and the behavior probably won't continue all season. (Don't coat the branch wounds with anything.) Fortunately, it's rare for squirrels to cause serious, long-term damage to trees.

Miri