An anchoring system includes a housing having a radial opening therein, and a piston disposed within the housing which is axially movable therein. A slip is in operable communication with the piston such that movement of the piston in a first axial direction relative to the housing causes movement of the slip in a first radial direction relative to the housing to anchor the anchoring system to a structure and movement of the piston in a second axial direction allows the slip to move in a second radial direction that allows unanchoring of the anchoring system. A sleeve is configured to cause movement of the piston in the second axial direction when moved in the second axial direction relative to the housing, in response to either mechanically pulling the sleeve in the second axial direction or increasing pressure applied against the piston.