  One of the proposed ground states of monolayer WTe$_2$, a two-dimensional
topological insulator, is an excitonic condensate. However, time-reversal
preserving and breaking solutions are competing at the mean-field level of
analysis, and it is unclear which condensate, if any, is realized in nature. In
this work we analyze the experimental signatures that allow to provide evidence
for the excitonic ground states and to distinguish between the two types of
condensates using scanning tunneling microscopy. We provide clear experimental
signatures in local mapping and quasiparticle interference patterns that
visualize the expected changes in local charge and spin density, and
characterize allowed backscattering processes in the presence of impurities and
disorder. Our results will thus help in the determination of the nature of the
WTe$_2$ ground state.
