High-quality reconstructions of the three-dimensional velocity and density fields of the local Universe are essential to study the local large scale structure. In this paper, the Wiener Filter reconstruction technique is applied to galaxy radial peculiar velocity catalogues to understand how the Hubble constant (H_0) value and the grouping scheme affect the reconstructions. While H_0 is used to derive radial peculiar velocities from galaxy distance measurements and total velocities, the grouping scheme serves the purpose of removing non-linear motions. Two different grouping schemes (based on the literature and a systematic algorithm) as well as five H_0 values ranging from 72 to 76 km s^−1 Mpc^−1 are selected. The Wiener Filter is applied to the resulting catalogues. Whatever grouping scheme is used, the larger H_0 is, the larger the infall on to the local volume is. However, this conclusion has to be strongly mitigated: a bias minimization scheme applied to the catalogues after grouping suppresses this effect. At fixed H_0, reconstructions obtained with catalogues grouped with the different schemes exhibit structures at the proper location in both cases but the latter are more contrasted in the less aggressive scheme case: Having more constraints permits an infall from both sides on to the structures to reinforce their overdensity. Such findings highlight the importance of a balance between grouping to suppress non-linear motions and preserving constraints to produce an infall on to structures expected to be large overdensities. Such an observation is promising to perform constrained simulations of the local Universe, including its massive clusters.