We demonstrate atomic layer deposition of high-quality dielectric HfO2 films on graphene and determine the magnitude of remote oxide surface phonon scattering in dual-oxide structures. The carrier mobility in these HfO2-covered graphene samples reaches 20,000 cm2/V s at low temperature. Distinct contributions to the resistivity from surface optical phonons in the SiO2 substrate and the HfO2 overlayer are isolated. At 300 K, surface phonon modes of the HfO2 film centered at 54 meV limit the mobility to approximately 20,000 cm2/V s.