We study matter accretion in a static, axially symmetric and vacuum geometry describing the exterior gravitational field of a black hole mimicker called the γ metric. We evaluate the thermal and optical properties of thin accretion disks, including the emission rate, luminosity and shadow, in the gamma spacetime. Also, we explore the radial accretion of polytropic matter fields onto the central source and evaluate the thermal and optical properties of the infalling gas, such as temperature and luminosity. The results are discussed in the context of evaluating the possibility that the true nature of astrophysical black hole candidates may not be a black hole but some exotic compact object possessing a non-vanishing mass quadrupole moment.