The problem of globular polymer unfolding under applied force is a widely-studied fundamental topic in biological and chemical physics, with important applications in cell biology. Much of the existing theoretical and experimental literature focuses on the case where force is applied while fixing the opposite end of the polymer chain in space. However, in a realistic biological microenvironment, forces will be applied against viscoelastic references, and the deformation of the folded polymer chain will be combined with the deformation of viscoelastic substrate. In this paper, we consider several simple viscoelastic models for the substrate, and show that its relaxation properties determine the unfolding kinetics. In particular, for low pulling forces, substrates with longer relaxation times cause lower unfolding rates for the pulled polymer chain, whereas for high forces, those substrates with longer relaxation times instead produce higher unfolding rates.