I have read much about taking off branches and healing the tree. I wonder if there is not more going on here. And I wonder where to actually prune as this just seems to be bigger than a dying branch, as possibly a quarter to a third of the bark around the main trunk is gone or seems loose. What to do?
Dying Dogwood Branch
Certified GKH Gardening Expert
It would appear that the bark peeling is due to some disease or pest issue with your tree.
You may want to have the tree inspected by a certified Arborist to determine the best coarse of action.
Here are some links with more information.