Humm, these are plants. They are both Tillansia (air-plants). I would guess the only way to kill it would also damage your trees. You might be able to safely spay it all with a powerful herbicide in the winter, when the trees are dormant, but you really need to contact your Extension Service and get some professonal advice. I grow the Spanish moss on purpose, and actually nourish it throughout the year. We don't have it growing "naturally" here in NE Mississippi. I love it to drape some of my mounted tropical plants with.
Where are you located? You need to consider at least adding this information so we all know when responding to you.
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