Answer:
The glycosaminoglycan they're referring to is probably heparin. Heparin is a molecule that binds to the glycoprotein antithrombin. Antithrombin functions to inhibit factor Xa and factor IIa (thrombin). Factor Xa produces thrombin from prothrombin, and thrombin forms fibrin from fibrinogen, which is the main component of clots.
When heparin binds to antithrombin, it strongly increases antithrombin activity, significantly inhibiting the downstream production of fibrin and the clots it forms. In this way, heparin acts as an anticoagulant. By inhibiting the pathways the promote clot formation, the countering pathways promoting clot breakdown predominate and the over time the body will break down the clot.
