The electronic properties of graphene can be significantly influenced by mechanical strain. One practical approach to induce strain in graphene is to transfer atomically thin membranes onto pre-patterned substrates with specific corrugations. The possibility of using nanoparticles to impart extrinsic rippling to graphene has not been fully explored yet. Here we study the structure and elastic properties of graphene grown by chemical vapour deposition and transferred onto a continuous layer of SiO2 nanoparticles with diameters of around 25 nm, prepared on a Si substrate by the Langmuir-Blodgett technique. We show that the corrugation of the transferred graphene, and thus the membrane strain, can be modified by annealing at moderate temperatures. The membrane parts bridging the nanoparticles are suspended and can be reversibly lifted by the attractive forces between an atomic force microscope tip and graphene. This allows the dynamic control of the local morphology of graphene nanomembranes.