**Core Concept**
Secondary allograft rejection occurs when the immune system recognizes and responds to the transplanted organ as foreign, leading to a more vigorous and destructive immune response. This type of rejection is mediated by memory T cells and is often antibody-independent. The underlying mechanism involves the activation of cytotoxic T cells and the release of cytokines that promote inflammation and tissue damage.

**Why the Correct Answer is Right**
The correct answer is mediated by memory T cells, specifically CD8+ cytotoxic T cells, which recognize and bind to the major histocompatibility complex (MHC) molecules on the surface of the allograft. This recognition triggers a cascade of events, including the release of perforin and granzymes, which ultimately lead to the lysis and destruction of the allograft cells. The secondary rejection response is also characterized by the activation of macrophages and the release of pro-inflammatory cytokines, such as TNF-α and IFN-γ.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option may refer to primary allograft rejection, which is mediated by naive T cells and is often antibody-dependent.
* **Option B:** This option may refer to chronic allograft rejection, which is a result of long-term immune activation and fibrosis, but is not primarily mediated by memory T cells.
* **Option D:** This option may refer to antibody-mediated rejection, which is a type of rejection that occurs in the presence of donor-specific antibodies, but is not the primary mechanism of secondary allograft rejection.

**Clinical Pearl / High-Yield Fact**
It's essential to note that secondary allograft rejection is often more difficult to diagnose than primary rejection, as the symptoms may be non-specific and the rejection response may be more subtle. A high index of suspicion and regular monitoring of graft function and immune markers are crucial for early detection and treatment of secondary rejection.

**Correct Answer:** C.