With the prospect of large volume radio neutrino detectors such as RNO-G and IceCube-Gen2, measuring neutrinos above PeV energies is within reach. At these energies, atmospheric muons stemming from cosmic ray air showers represent a rare background: They penetrate the ice and can mimic the interaction of a neutrino through catastrophic energy losses. Due to both limited experimental measurements and limited modeling in hadronic interaction models, the expected event rate is subject to large uncertainties. In this study, we predict rates and associated uncertainties and evaluate mitigation strategies, such as parent air shower detection.