Aquifer remediation is a challenging problem with environmental, social, and economic implications. As a general rule, pumping proceeds until the concentration of the target substance within the pumped water lies below a prespecified value. In this paper we estimate the a priori potential failure of the endpoint of remediation due to a rebound of concentrations driven by back diffusion. In many cases, it has been observed that once pumping ceases, a rebound in the concentration at the well takes place. For this reason, administrative approaches are rather conservative, and pumping is forced to last much longer than initially expected. While a number of physical and chemical processes might account for the presence of rebounding, we focus here on diffusion from low water mobility into high mobility zones. In this work we look specifically at the concentration rebound when pumping is discontinued while accounting for multiple mass transfer processes occurring at different time scales and parametric uncertainty. We aim to develop a risk‐based optimal operation methodology that is capable of estimating the endpoint of remediation based on aquifer parameters characterizing the heterogeneous medium as well as pumping rate and initial size of the polluted area.