Final answer:
CD8+ cytolytic T lymphocytes recognize and destroy virus-infected cells because these cells present viral antigens bound to class I MHC molecules on their surfaces, enabling CTLs to detect and target them.
Step-by-step explanation:
CD8+ cytolytic T lymphocytes (CTLs) can recognize and kill virus-infected mucosal epithelial cells because mucosal epithelial cells, like all nucleated cells, express class I MHC molecules. These cells are capable of processing cytoplasmic viral proteins and presenting complexes of class I MHC molecules bound with viral peptides on their cell surfaces. Once these viral antigens are presented on the surface of infected cells, CTLs can recognize these antigens as foreign and initiate the process of killing the infected cells. This immune response is critical for controlling and eliminating viral infections within the body.