Dogwood tree branches
It is fine to cut them off now. Just be sure to cut back to a bud or side branch, or remove them at the trunk. If you make good, clean cuts with sharp pruning tools, wound dressing is not necessary. If fact, research has shown that wound dressing interferes with a tree's natural ability to seal off such wounds. There are a very few instances where wound dressing is recommended to minimize insect problems, but not for dogwoods.