**Core Concept**
The question is testing the student's knowledge of the anatomy of the knee joint and the structures that can cause a cystic enlargement. The correct answer involves understanding the bursae and their role in reducing friction between the tendons and bones of the knee.

**Why the Correct Answer is Right**
The structure most likely to be enlarged in this scenario is the **prepatellar bursa**, but given the location on the back of the knee, it is more likely to be the **popliteal bursa**. The popliteal bursa is located between the tendon of the gastrocnemius muscle and the femur, and its enlargement can cause a fluid-filled cystic structure that limits knee mobility. This condition is often associated with chronic irritation or inflammation of the bursa, which can be caused by repetitive strain or pressure on the knee joint.

**Why Each Wrong Option is Incorrect**
* **Option A:** The infrapatellar fat pad is a fatty structure located below the patella, and while it can become inflamed or irritated, it is not typically associated with a cystic enlargement that limits knee mobility.
* **Option B:** The iliotibial (IT) band is a ligament that runs down the outside of the thigh from the hip to the knee, and while it can cause friction and irritation, its enlargement is not typically characterized by a fluid-filled cystic structure.
* **Option D:** The Baker's cyst is a type of popliteal cyst that can cause a fluid-filled swelling on the back of the knee, but the question is asking for the underlying structure that is enlarged, not the clinical manifestation.

**Clinical Pearl / High-Yield Fact**
When evaluating a patient with a cystic swelling on the back of the knee, it's essential to consider the possibility of a popliteal bursa enlargement, which can be caused by chronic irritation or inflammation of the bursa. A thorough physical examination, including palpation and range of motion, can help confirm the diagnosis.

**Correct Answer: C. popliteal bursa**