This is the second part of our study of the background impurity influence on the intersubband energy structure of a single SiGe/Si/SiGe quantum well with the impurity delta layer within the well. By the background impurity we mean sparse shallow donor doping throughout the infinitely wide barriers. In this part we consider a situation where the delta layer is positioned near the edge of the well and the structure symmetry is broken. We explain in detail the necessary modifications of our self-consistent method that includes calculation of impurity binding energy. The results particularly show that the mentioned asymmetry combined with the background impurity in the barriers provides new features to the effect of tuning the intersubband optical transitions by the ionization grade of the impurity in delta-layer that provides new technological possibilities.