The Fluorescence Detector (FD) of the Pierre Auger Observatory has a large exposure to search for upward-going showers. Constraints have been recently obtained by using 14 years of FD data searching for upward-going showers in the zenith angle range $[110^\circ, 180^\circ]$.
In this work, we translate these bounds to upper limits of a possible flux of ultra high energy tau-leptons escaping from the Earth into the atmosphere.
Such a mechanism could explain the observation of "anomalous pulses" made by ANITA, that indicated the existence of upward-going air showers with energies above $10^{17}$ eV.
As tau neutrinos would be absorbed within the Earth at the deduced angles and energies, a flux of upward-going taus could only be resulted from an unknown type of ultra high energy Beyond Standard Model particle penetrating the Earth with little attenuation, and then creating tau-leptons through interactions within a maximum depth of about 50 km before exiting.
We test classes of such models in a generic way and determine upper flux limits of ultra high energy BSM particles as a function of their unknown cross section with matter.