Answer: Carissa hollies are often grafted onto an Ilex rootstock for more vigorous growth. The leaves you describe sound like they're coming from below the graft. Trace the branches down to see where they are attached to the plant. If they're orginating from below the graft (swelling) on the main stem, they're coming from the root stock and not from the carrisa. Prune them off where they originate.
Best wishes with your landscape!
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