We report an extensive study of the magnetotransport properties of magnetically doped two-dimensional hole systems. Inverted manganese modulation doped InAs quantum wells with localized manganese ions providing a magnetic moment of S=5/2 were grown by molecular beam epitaxy. Strong localization effect found in low-field magnetotransport measurements on these structures can either be modified by the manganese doping density or by tuning the two-dimensional hole density p via field effect. The data reveal that the ratio between p and manganese ions inside or in close vicinity to the channel enlarges the strong localization effect. Moreover, asymmetric broadening of the doping layer due to manganese segregation is significantly influenced by strain in the heterostructure.