**Core Concept**
The auriculotemporal nerve is a branch of the mandibular division of the trigeminal nerve (cranial nerve V) that provides sensory innervation to the temporomandibular joint, the external auditory meatus, and the tympanic membrane. It also carries parasympathetic fibers from the otic ganglion to the parotid gland, which regulate salivary secretion.

**Why the Correct Answer is Right**
The injury to the auriculotemporal nerve during parotid tumor removal could result in Frey's syndrome, also known as gustatory sweating or auriculotemporal syndrome. This condition occurs due to the aberrant regeneration of parasympathetic fibers from the auriculotemporal nerve to the sympathetic fibers of the sympathetic plexus surrounding the external carotid artery. As a result, the parasympathetic fibers stimulate the sweat glands and arrector pili muscles in the skin of the face, causing excessive sweating and flushing in response to stimuli that normally induce salivation, such as the sight or smell of food.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is not relevant to the scenario described.
* **Option B:** Injury to the auriculotemporal nerve does not typically result in trigeminal neuralgia, which is a condition characterized by sudden, severe pain in the face.
* **Option C:** Frey's syndrome is not a complication of damage to the facial nerve, which controls facial expressions and taste to the anterior two-thirds of the tongue.

**Clinical Pearl / High-Yield Fact**
Frey's syndrome is a classic complication of parotid surgery, and its development can be minimized by precise surgical technique and avoidance of injury to the auriculotemporal nerve.

**Correct Answer:** C. Frey's syndrome.