The impact on the electronic and structural properties of chemical vapor deposition (CVD) graphene transferred onto SiO2/silicon (Si) of continuous H2-based plasmas, used to remove sticky residues composed of poly(methyl methacrylate) (PMMA) and Si-based nanoparticles at the surface, was investigated. By combining X-ray photoelectron spectroscopy (XPS) and atomic force microscopy (AFM), we found that H2 plasma treatment, which allows the simultaneous etching of Si-based nanoparticles and PMMA, causes fragmentation of a CVD graphene layer into nanoplatelets and subsequent etching of the uncovered SiO2/Si surface. We added CF4 to the H2 plasma to allow the selective etching of Si-based impurities while maintaining the quality and stability of the CVD graphene. The increase in the sp2/sp3 ratio and decrease in the Si–C bonds, evaluated from XPS analysis, reveal the removal of all residual contamination. AFM analysis confirms the efficient and selective etching of residues from the surface of graphene, which displays a microscopic corrugation due to a weak coupling with the SiO2/Si substrate. The established CF4/H2 plasma processing generates, however, cracks along the grain boundaries in CVD graphene, which is responsible for the unusual transport properties. Characterization of local chemical structures using Raman spectroscopy reveals that the CVD graphene layer is essentially undamaged under the CF4/H2 plasma and dehydrogenation is incomplete in the subsequent annealing at 400 °C. The local electronic structure is probed using reciprocal-space photoemission electron microscopy (k-PEEM) and reveals a small, negative shift below 0.1 eV of the Dirac point with respect to the Fermi level, which is consistent with n doping caused by trapped hydrogen species at the interface. Threshold photoemission electron microscopy (PEEM) analysis establishes the work function of CVD graphene as 4.57 eV. This study reveals that the optimized cleaning process almost recovers the original properties of quasi-freestanding graphene.