Which of these describes a situation where extirpation would be necessary?

Extirpation refers to the surgical removal of a tumor or a mass from an organ or tissue. In the context of the choices provided, the act of removing a tumor directly aligns with the definition of extirpation. This procedure is necessary when there is a presence of malignancy or abnormal growth, which can pose a risk to the patient's health.

The other options focus on different medical procedures that do not involve the surgical removal of tissue or abnormal growth. For instance, repairing damaged tissue or assessing a patient's condition does not necessitate the complete removal of a structure, and transferring blood is unrelated to the concept of removing tissue or tumors. Thus, the option to remove a tumor clearly exemplifies a situation where extirpation is necessary.