Adiabatic and radiative effects accompanying interactions of a kink with a point-like impurity are studied by means of the perturbation theory within the framework of a model of a damped DC-driven charge-density-wave system based on a perturbed sine-Gordon equation. A threshold (maximum) value of the DC voltage (external drive applied to the system) admitting capture of a kink (charged soliton) by an impurity is found. The maximum voltage allowing the existence of pinned states of the kink is also found, and the corresponding dependence of the density of released kinks on the voltage is evaluated, provided that the coordinate of an individual impurity relative to an underlying lattice is a uniformly distributed random quantity. It is demonstrated that this dependence gives rise to an additional peculiar branch of the current-voltage characteristic (CVC) of the system. The energy emitted by a moving kink during its collision with the impurity is calculated. It is shown that, provided that the level of direct dissipative losses is sufficiently low, the radiative losses render the CVC hysteretic.