Optical interrogation of tissues is broadly considered in biomedical applications. Nevertheless, light scattering by tissue limits the resolution and accuracy achieved when investigating sub-surface tissue features. Light carrying optical angular momentum or complex polarization profiles, offers different propagation characteristics through scattering media compared to light with unstructured beam profiles. Here we discuss the behaviour of structured light scattered by tissue-mimicking phantoms. We study the spatial and the polarization profile of the scattered modes as a function of a range of optical parameters of the phantoms, with varying scattering and absorption coefficients and of different lengths. These results show the non-trivial trade-off between the advantages of structured light profiles and mode broadening, stimulating further investigations in this direction.