Final answer:
The thymus gland is responsible for T lymphocyte production, and its surgical removal is called a thymectomy, which is the correct answer to the student's question.
Step-by-step explanation:
The gland responsible for the production and maturation of T lymphocytes is the thymus gland.
The thymus is a bi-lobed organ located just above the heart and is involved in the immune system's adaptive component, facilitating the maturation of T cells, which are critical for the body's defense against pathogens. The surgical removal of the thymus gland is known as a thymectomy. This procedure would impact T cell production since the thymus is the site where immature T cells, or thymocytes, mature into functional T cells capable of mounting an immune response.
Therefore, the correct answer to the given question, "Cutting out the gland that is responsible for the production of T lymphocytes is," would be (a) Thymectomy.