Using a suite of numerical calculations, we consider the long-term evolution of circumbinary debris from the Pluto--Charon giant impact. Initially, these solids have large eccentricity and pericenters near Charon's orbit. On time scales of 100--1000 yr, dynamical interactions with Pluto and Charon lead to the ejection of most solids from the system. As the dynamics moves particles away from the barycenter, collisional damping reduces the orbital eccentricity of many particles. These solids populate a circumbinary disk in the Pluto-Charon orbital plane; a large fraction of this material lies within a `satellite zone' that encompasses the orbits of Styx, Nix, Kerberos, and Hydra. Compared to the narrow rings generated from the debris of a collision between a trans-Neptunian object (TNO) and Charon, disks produced after the giant impact are much more extended and may be a less promising option for producing small circumbinary satellites.