**Core Concept**
The fascia covering the rectus abdominis muscle is a layer of connective tissue that provides support and separates the muscle from surrounding structures. This fascia is a part of the deeper abdominal wall and plays a crucial role in maintaining abdominal wall integrity.

**Why the Correct Answer is Right**
The correct answer is the **transversalis fascia**. This is because the rectus abdominis muscle is enveloped by the transversalis fascia, which is a layer of fascia that lies deep to the rectus sheath. The transversalis fascia is a dense, fibrous layer that provides a strong attachment point for the rectus abdominis muscle and helps to maintain the shape of the abdominal wall.

**Why Each Wrong Option is Incorrect**
* **Option A:** The **rectus sheath** is a composite layer of aponeuroses that envelops the rectus abdominis muscle, but it is not the fascia that directly covers the muscle.
* **Option B:** The **fascia iliaca** is a layer of fascia that covers the iliopsoas muscle, not the rectus abdominis muscle.
* **Option C:** The **peritoneum** is a serous membrane that lines the abdominal cavity and covers the viscera, but it is not the fascia that directly covers the rectus abdominis muscle.

**Clinical Pearl / High-Yield Fact**
It is essential to remember that the rectus abdominis muscle is enveloped by the transversalis fascia, which is a critical layer for maintaining abdominal wall integrity.

**Correct Answer: C. Transversalis fascia**