Leeches have been used in microvascular surgery since the 1980's.  One problem that may be encountered in during a surgery to replant a finger or thumb is congestion or clotting in the venous system.  If the veins clot, the area that has been re-attached doesn't drain sufficiently which could eventually lead to the amputated digit dying. 

Leeches secrete a substance called hirudin that has a anticoagulation (stops clotting) effect. When a surgeon notices that the replanted digit is congested he may initiate leech therapy.  When the leech is placed on the congested digit it attaches and naturally injects the hirudin to begin drawing blood out of the digit. This process moves blood through the congested digit, allowing it to recover. Leech therapy may only be required intermittently for a few days for the blood supply to recover.