We have investigated the anisotropic magnetic responses of a 2D-superconducting Bi2Te3/FeTe heterostructure. Cross-sectional STEM imaging revealed that the excess Fe atoms in the FeTe layer occupy specific interstitial sites. They were found to show strong anisotropic magnetic responses under a magnetic field either perpendicular or parallel to the sample surface. Under perpendicular magnetic fields within 1000 Oe, conventional paramagnetic Meissner effect, superconducting diamagnetism, and anomalous enhancement of magnetization successively occur as the magnetic field increases. In contrast, under parallel magnetic fields, superconducting diamagnetism was not observed explicitly in the magnetization measurements and the anomalous enhancement of magnetization appears only for fields higher than 1000 Oe. The observed strong magnetic anisotropy provides further evidence that the induced superconductivity at the interface of the Bi2Te3/FeTe heterostucture has a 2D nature.