We study self-focusing and group-velocity dispersion (GVD) effects in the inhomogeneous atmosphere on pulsed-laser space debris removal facilitated by a ground-based laser. It is found that changes of the pulse duration and the beam spot size with the propagation distance are noticeable due to the interplay of the GVD effect and the self-focusing effect, which is quite different from the behavior in the linear case. It is shown that the temporal pulse splitting may appear on the space debris, and the spatial side lobe usually appears together with the temporal pulse splitting. As compared with the linear case, the beam width and the pulse width on the debris target increase. On the other hand, crucial formulae of the modified focal length and the M2-factor for laser debris removal are also derived. It is found that the beam quality on the debris target becomes better if our modified focal length is adopted, and the beam quality on the debris target will be good if the value of M2-factor is less than 1.6.