  We infer dark matter properties from gamma ray residuals extracted using
eight different interstellar emission scenarios proposed by the Fermi-LAT
Collaboration to explain the Galactic Center gamma ray excess. Adopting the
most plausible simplified ansatz, we assume that the dark matter particle is a
Majorana fermion interacting with standard fermions via a scalar mediator.
Using this theoretical hypothesis and the Fermi residuals we calculate Bayesian
evidences, including Fermi-LAT exclusion limits from 15 dwarf spheroidal
galaxies as well. Our Bayes factors single out four of the Fermi scenarios as
compatible with the simplified dark matter model. In the most preferred
scenario the dark matter (mediator) mass is in the 100-500 (1-200) GeV range
and its annihilation is dominated by top quark final state. Less preferred but
still plausible is annihilation into b\bar{b} and tau^+tau^- final states with
an order of magnitude lower dark matter mass. Our conclusion is that the
properties of dark matter extracted from gamma ray data are highly sensitive to
the modeling of the interstellar emission.
