We apply the iterative MCS deconvolution method (ISMCS) to near-IR HST archives data of seven gravitationally lensed quasars currently monitored by the COSMOGRAIL collaboration: HE 0047-1756, RX J1131-1231, SDSS J1138+0314, SDSS J1155+6346, SDSS J1226-0006, WFI J2026-4536 and HS 2209+1914. In doing so, we obtain relative positions for the lensed images and shape parameters for the light distribution of the lensing galaxy in each system. The lensed image positions are derived with 1-2 mas accuracy. To predict time delays and to test the ability of simple mass models to reproduce the observed configuration, isothermal and de Vaucouleurs mass models are calculated for the whole sample using state-of-the-art modeling techniques. The effect of the lens environment on the lens mass models is taken into account with a shear term. Doubly imaged quasars are equally well fitted by each of these models. A large amount of shear is necessary to reproduce SDSS J1155+6346 and SDSS J1226-006. In the latter case, we identify a nearby galaxy as the dominant source of shear. The quadruply imaged quasar SDSS J1138+0314 is well reproduced by simple lens models, which is not the case for the two other quads, RX J1131-1231 and WFI J2026-4536. This might be the signature of astrometric perturbations due to massive substructures in the lensing galaxy unaccounted for by the models. Other possible explanations are also presented.