Motivated by the study of extreme mass-ratio binary systems, the use of curved backgrounds in computations of classical, gravitational amplitudes have recently appeared in the literature [2308.15304, 2308.14832]. While these investigations concern the self-force expansion, the use of curved backgrounds is interesting in its own right. In this talk, I discuss how one can use worldline quantum field theory and an expansion around the Schwarzschild–Tangherlini metric to reformulate the perturbative expansion of the Compton amplitude, which describes the scattering of a graviton off a compact object. Specifically, I address the curved computation of the first and second post-Minkowskian Compton amplitudes, and their consistency with flat space calculations.