In order to unravel the complex interplay between substrate interactions and film configuration, we investigate and characterize graphene on a support with non-three-fold symmetry, the square Ir(100). Below 500 °C, distinct physisorbed and chemisorbed graphene phases coexist on the surface, respectively characterized by flat and buckled morphology. They organize into alternating domains that extend on mesoscopic lengths, relieving the strain due to the different thermal expansion of film and substrate. The chemisorbed phase exhibits exceptionally large one-dimensional ripples with regular nanometer periodicity and can be reversibly transformed into physisorbed graphene in a temperature-controlled process that involves surprisingly few C-Ir bonds. The formation and rupture of these bonds, rather than ripples or strain, are found to profoundly alter the local electronic structure, changing graphene behavior from semimetal to metallic type. The exploitation of such subtle interfacial changes opens new possibilities for tuning the properties of this unique material.