What enzyme removes unneeded clots after healing has occurred?

The right answer is plasmin.

Plasmin is a peptidase that catalyzes the hydrolysis of peptide bonds located preferentially after a lysine residue or an arginine residue. In this respect, it has greater selectivity than trypsin.

This enzyme intervenes by lysing fibrin in the process of fibrinolysis, an essential step of blood coagulation. It is derived from the activation of plasminogen by urokinase and tissue plasminogen activator.