Final answer:
The masseter muscle is most likely to be tender or damaged in a patient with moderate tenderness on closing their jaw after a cheekbone injury, as it is the primary muscle responsible for elevating the mandible to close the mouth during chewing.
Step-by-step explanation:
The muscle that is most likely to be damaged or tender when a client presents with moderate tenderness on closing their jaw after a broken cheekbone would be the masseter muscle. The masseter is the main muscle involved in chewing and it elevates the mandible to close the mouth. This muscle, along with the temporalis, works to elevate and close the jaw, but given the location near the cheekbone and its primary function in mastication, the masseter is more likely to be the source of tenderness in this scenario.