Final answer:
The carcinoembryonic antigen (CEA) blood test is used to determine if the client is experiencing occult bleeding from the gastrointestinal tract.
Step-by-step explanation:
The nurse should respond to the client by saying that the CEA determines if you are experiencing occult bleeding from the gastrointestinal tract. CEA, or carcinoembryonic antigen, is a tumor marker that is produced by tumors of the gastrointestinal system, among other types of cancer. A rising CEA level in a patient with a history of treated bowel cancer can indicate the return of the cancer, often before it can be detected by imaging or examination.