Answer: I don't think the moths have anything to do with the dead branches. When individual branches die, they generally have an internal cause; either damage at the main trunk, or some problems with the roots. I'd prune out the dead branches and watch the holly carefully for healthy new growth. As long as it is producing new stems, foliage, flowers and berries, it is healthy and the loss of a few branches shouldn't harm it. If the growth slows or stops, or if there is a general decline in its health, there may be problems with the roots. Keep your fingers crossed that the dead branches are just isolated damage and won't spread to the rest of your holly.
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