"DMSA diminishes the production of bile duct, pancreas and liver lesions and inhibits the development of fibrosis of the pancreas and cirrhosis of liver in lab animals exposed to these toxic chemicals. The decrease in the biliary excretion of these compunds by DMSA seems to be the reason for the pronounced protective effects of DMSA on the bile duct, pancreas and liver."
Here they are saying that DMSA is actually protective of the liver.
Anything you take into your body will likely interact with the liver at some point. But for most people, the primary concern with DMSA chelation is the kidneys, not the liver. If your liver is sensitive to DMSA, then indeed there are some issues that need to be resolved there.