Though carrying considerable economic and societal costs, restricting individuals' traveling freedom appears as a logical way to curb the spreading of an epidemic. However, whether, under what conditions, and to what extent travel restrictions actually exert a mitigating effect on epidemic spreading are poorly understood issues. Recent studies have actually suggested the opposite, i.e., that allowing some movements can hinder the propagation of a disease. Here, we explore this topic by modeling the spreading of a generic contagious disease where susceptible, infected, or recovered point-wise individuals are uncorrelated random-walkers evolving within a space comprising two equally sized separated compartments. We evaluate the spreading process under different separation conditions between the two spatial compartments and a forced relocation schedule. Our results confirm that, under certain conditions, allowing individuals to move from regions of high to low infection rates may turn out to have a positive effect on aggregate; such positive effect is nevertheless reduced if a directional flow is allowed. This highlights the importance of considering travel restriction policies alternative to classical ones.