Adequate Summer water...give it a good soaking once twice a month or as needed. Put a hose at the base, set it at just a slow dribble so that water doesn't pool and run off, let it go for .5 hour. I'd weed an area around the base of the tree, and put down some bark mulch which will help buffer moisture loss.
Monitor the leaf health, dogwoods show moisture stress readily and its easy to see. Look for leaf keeling (the leaves cup like a partially closed clamshell), leaf tip burn, and leaf discoloration.
The good news is that there is more robust new growth, the old, finer twiggy growth from its days in the nursery pot probably just could not handle the new location. Tiny diameter branches are susceptible to even minor amounts of damage, shading, or water stress are aborted by the plant when they are no longer productive. That happens to both crowded inner branches and lower shaded branches in dogwoods. Its generally not a cause for concern, except in your case where the tree is a juvenile.