Catalysis is usually construed to facilitate equilibrium being attained more easily and quickly, or occasionally less so (anticatalysis), but not to alter the position of equilibrium, i.e., not to alter the equilibrium constant Keq. Indeed, it is sometimes stated that if catalysis could alter Keq, then it could be employed to violate the Second Law of Thermodynamics. Nevertheless, cases wherein catalysis does alter Keq are known. This has been dubbed epicatalysis. A violation of the Second Law via epicatalysis is precluded if it costs at least as much work to restore the catalyst (specifically, the epicatalyst) to its initial state as can be yielded by the alteration of Keq that it can achieve. In most cases of epicatalysis, it does cost at least as much work usually more work to restore the catalyst (specifically, the epicatalyst) to its initial state as can be yielded by the alteration of Keq that it can achieve. Yet recently systems and processes entailing epicatalysis have been investigated for which this may not be true, and hence which may challenge the Second Law. In this paper we investigate a system wherein catalysis alters Keq, yet wherein at least prima facie there seems to be at least in principle zero thermodynamic cost-zero required work for withdrawal and re-insertion of catalysis. Since chemical systems and reactions can be complex, in this paper we instead investigate a simple mechanical-gravitational system that may serve to illustrate the principles more transparently. This system consists a gas particle (e.g., molecule, Brownian particle, etc.) capable of moving within and between two gravitational potential wells separated by a barrier, in a uniform gravitational field.