The adenoids, tonsils, appendix, and spleen are all part of the lymphatic system, which plays a crucial role in immune function and the filtration of pathogens. These organs contribute to the body's defense by trapping and eliminating bacteria and other pathogens.

Adenoids and tonsils are lymphatic tissues located in the throat and help prevent infection by filtering pathogens from inhaled or ingested particles.

The appendix contains lymphoid tissue and is thought to play a role in gut immunity.

The spleen filters blood, removing old or damaged blood cells and producing lymphocytes for immune response.

The other options are unrelated:

B. Gastrointestinal: Involved in digestion, but not specifically immune response.

C. Cardiovascular: Involved in blood circulation, not immune response.

D. Nervous: Coordinates sensory and motor functions, unrelated to lymphatic tissue.

Therefore, the correct answer is A. Lymphatic.