Recent study of a high-mobility 2D hole gas in a strained Ge quantum well revealed strong transport anisotropy in the quantum Hall regime when the magnetic field was tilted away from the sample normal. In the present study we demonstrate that the anisotropy persists to such high temperatures and filling factors that quantum oscillations are no longer observed. This finding rules out the formation of a stripe phase as a possible origin for the observed anisotropy. However, we also show that the observed anisotropy is not consistent with other known anisotropies, such as those arising from finite thickness effects or surface roughness.