Fortunately, the plants don't need a cure as they are not diseased and the larvae are a passing phenomenon. The shrubs will leaf-out normally next year, and this level of premature leaf loss, this late in the summer, is of little consequence to their long-term vigor. These are Dogwood Sawfly larvae, and while they look just like caterpillars, sawflies are unrelated to butterflies and moths. This distinction matters when it comes to some of the lower-toxicity pesticide choices, as active ingredient B.t.k. used for caterpillars won't work with sawflies, but ingredient spinosad should. Even so, this time of year the larvae are nearly done feeding, so there is little value in spraying. (Especially since there are hardly any leaves left to treat.) What's left of the chewed leaves will shed soon, and the shrubs will likely not (and should not be encouraged to) produce replacement foliage this late in the season. Next year, you can monitor for when the larvae tend to appear around midsummer and begin hand removal or treatments at that time, to manage them before populations reach defoliating levels.

As a native insect, this sawfly species serves as food for a wide range of predators, likely including songbirds and numerous other beneficial insects. Tolerating low levels of their presence may be best to support wildlife in the area, though understandably you wouldn't want the entire shrubs denuded each year. Many insects experience population booms and crashes based on weather and predator/parasite numbers, so it's not likely they will be problematic each year hereafter. Finding them when young and either physically removing them or conservatively spraying at that time can help avoid an outbreak large enough to cause this level of defoliation.

Horticultural oil is recommended over neem oil, but the difference between them may not be too great if sawflies are listed on both product labels as insects controlled. Each needs to contact the pest directly in order to have an impact on it, so since sawfly larvae tend to feed on the sheltered undersides of foliage, sprays need to reach them there, and coverage needs to be thorough on all foliage surfaces. This is difficult to achieve when the undersides of leaves need to be coated, and may be why your prior neem treatments were insufficient.

If you wish to transplant the shrubs to another part of the yard rather than treat for or risk future outbreaks, you could use any number of alternative species in its place - whichever fit the space and suit the site conditions - since this insect does not feed on other host plants outside of Cornus.

Miri