Is Lymph is pumped through the lymphatic system by your heart?

False.

Lymph is pumped through the lymphatic system by the contraction of skeletal muscles and the movement of the diaphragm during breathing, not by your heart. The lymphatic system is a network of vessels and nodes that helps to remove waste and toxins from the body. It is a one-way system that flows towards the heart, and the lymph is moved along by the contractions of the muscles and the movement of the diaphragm.