They also eat poison ivy, so I can recycle that terrible plant. It normally has quite a nice display. There is nothing you can do to discourage the plant. The odds are that it will have flowers in the spring, though perhaps not as much as last year. Still, enjoy the bloom now.
Dogwood trees have shallow roots.
I'd plant only very shallow rooted perennials there, for instance sweet woodruff or Japanese roof iris, and not hostas, for instance. Planted several types of perennials last spring and this fall. The squirrels are tearing the garden up and I have seen several voles in the early morning and late afternoon. The squirrels are also chewing up the newly seeded lawn. But perhaps a dog will discourage the former.