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Motivated by recent experimental results on the topological iron-based superconductor FeSeTe, we examine the zero energy Shiba states in this compound. We show that, inside the superconducting phase, the orbital structure of the low-energy states near the Fermi energy leads to formation of zero-energy Shiba states close to the magnetic impurities. We compare the properties of such zero energy Shiba states with the available experimental results on this system. In particular, we show that the energy of Shiba states are highly sensitive to the location of the magnetic impurity in the unit cell. Moreover, the anomalous coupling of Shiba states near two nearby magnetic impurities is also discussed.