**Core Concept**
Median nerve lesions at the wrist, also known as carpal tunnel syndrome, result from compression of the median nerve as it passes through the carpal tunnel. This compression can lead to various neurological symptoms due to damage to the nerve fibers. The median nerve innervates muscles and skin areas in the hand, forearm, and thumb.

**Why the Correct Answer is Right**
The median nerve is responsible for innervating the thenar muscles (thumb muscles), specifically the opponens pollicis, abductor pollicis brevis, and flexor pollicis brevis. Compression of the median nerve at the wrist can lead to weakness or paralysis of these muscles, resulting in impaired thumb opposition, abduction, and flexion. Additionally, median nerve compression can cause sensory symptoms, such as paresthesia (tingling) and numbness, in the palmar aspect of the thumb, index, middle finger, and the radial half of the ring finger.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because the median nerve does indeed innervate the thenar muscles, which are responsible for thumb movement and sensation. Loss of these functions is a hallmark of median nerve compression.
**Option B:** This option is incorrect because the median nerve is responsible for the innervation of the palmar cutaneous branch, which provides sensation to the palmar aspect of the thumb, index, middle finger, and the radial half of the ring finger. Compression of the median nerve can lead to sensory deficits in this distribution.
**Option C:** This option is incorrect because the ulnar nerve, not the median nerve, is responsible for the innervation of the hypothenar muscles (little finger muscles) and the interosseous muscles, which are involved in finger movement and sensation.

**Clinical Pearl / High-Yield Fact**
In patients with suspected carpal tunnel syndrome, a useful clinical examination finding is Tinel's sign, which involves lightly tapping the median nerve at the wrist to elicit paresthesia or tingling in the distribution of the median nerve. This sign can aid in diagnosing median nerve compression at the wrist.

**Correct Answer:** A.