Involved in restoring normal CheY-P levels by dephosphorylating CheY-P. Inhibits CheD by incorporating in its fold a structural motif that mimics a CheD substrate recognition site to bait and inactivate it. Heterodimer with CheD. The CheC-CheD heterodimer interacts with phosphorylated CheY. The CheC-CheD dimer has higher phosphatase activity than CheC alone. Belongs to the CheC family.