The distortion due to a fixed point impurity with variable charge placed in the center of a classical harmonically confined two-dimensional (2D) large Coulomb cluster is studied. We find that the net topological charge (N(-)-N+ ) of the system is always equal to six independent of the position and charge of the impurity. In comparison with a 2D cluster without impurity charge, only the breathing mode remains unchanged. The screening length is found to be a highly nonlinear function of the impurity charge. For values of the impurity charge smaller than the charge of the other particles, the system has almost the same screening strength. When the impurity charge is larger, the screening length is strongly enhanced. This result can be explained by the competition between the different forces active in the system.