Final answer:
The basement membrane, located below the stratum basale, is responsible for the strong attachment between the epidermis and dermis, aided by dermal papillae which increase the connection's strength.
Step-by-step explanation:
The structure responsible for the strength of attachment between the epidermis and dermis is known as the basement membrane. This membrane is a layer that lies directly below the stratum basale, which is the deepest layer of the epidermis.
The cells of stratum basale bond to the dermis via intertwining collagen fibers, facilitating a strong connection. Additionally, finger-like projections called dermal papillae, found in the superficial portion of the dermis, increase the strength of this connection. The more extensive these folds, the stronger the bond between the epidermis and dermis. Hence, the correct answer to the student's question is 'C. basement membrane'.