Actual substrates unavoidably possess, to some extent, defects and dirt, which motivate understanding the impact due to their presence. The presence of a substrate naturally breaks symmetries. Additionally, it effectively reduces spatial dimensionality, which favors fluctuation-dominated behavior, but it also provides a multitude of possible interactions. We show evidence of novel behavior in the case of polymer mass transport at a crystalline substrate when a single attractive impurity is present. Specifically, we introduce a model system describing how an attractive impurity pins adsorbed polymers on a substrate. We propose a novel mechanism to explain the size scaling dependence of the diffusion coefficient as D∼N−3/2 for polymers with N monomers. Additionally, the size dependence of the diffusion coefficient scales can be described as D∼N−δ, with δ=1.51 as determined from extensive simulations.