We have used ultrahigh vacuum scanning tunneling microscopy (STM) to investigate the effect of thermal annealing of graphene grown by chemical vapor deposition on a Cu(110) foil. We show that the annealing appears to induce a reconstruction of the Cu surface along the [210] direction, with a period of 1.43 nm. Such reconstructions have been ascribed to the tensile strain induced in the Cu surface by its differential thermal expansion relative to the graphene over-layer, but we show that it is in fact a moiré pattern due to interference between the graphene and the underlying atomic lattice as evidenced by the appearance of an odd-even transition only observed due to misorientation of the top layer of a layered crystal. This highlights that the analysis of STM measurements of graphene on metal surfaces should take such interference effects into account and that the graphene-Cu interface is more complex than previously thought.