The splashback radius of a dark matter halo, which corresponds to the first apocenter radius reached by infalling matter and substructures, has been detected around galaxy clusters using a multitude of observational methods, including weak lensing measurements. In this manuscript, we present how the splashback feature in the halo density profile affects galaxy cluster masses derived through weak lensing measurements if it is not accounted for. We find that the splashback radius has an increasingly large effect on group-sized halos towards $M_{200m} ∼ 10^{13.5} \mathrm{M_\odot}$. Depending on the model and the radial scale used, the cluster/group masses can be biased low by more than 0.1 dex. This bias, in turn, would result in a slightly lower $Ω_m$ value if propagated into a cluster cosmology analysis. The splashback effect with group-sized dark matter halos may become important to consider, given the increasingly stringent cosmological constraints coming from optical wide-field surveys.