The semiclassical molecular orbital approximation modified by a proper electron translation factor has been employed to investigate the dynamics of the low-energy charge transfer between molecular hydrogen and a few stripped ions having charges . Freezing the molecular details of the target the colliding system has been treated as a quasi-diatomic molecule using the pseudo-potential technique that accounts for the effective binding of the electron in the combined nuclear field. Close-coupled equations are solved to obtain both the total and partial capture cross sections. The calculated total cross sections show good agreement with the available experimental measurements; the reported -distributions for and are new. A relative comparison for single-electron transfer from by other ions considered reveals the possible role of the projectile core; in the low-energy region the increasing core size affects considerably both the -distribution and the shape of the total capture cross sections. The projectile exhibits a distinctive role due to its finite core; the calculated total cross sections show oscillations in complete agreement with the experimental findings. The presence of a finite core enhanced the contribution to the lower -value substate of the final channel in accordance with the role of the Stark effect; the state-selective capture cross sections depend strongly on the size of the projectile core.