  The TRAPPIST-1 Habitable Atmosphere Intercomparison (THAI) is a community
project that aims to quantify how dfferences in general circulation models
(GCMs) could impact the climate prediction for TRAPPIST-1e and, subsequently
its atmospheric characterization in transit. Four GCMs have participated in
THAI so far: ExoCAM, LMD-Generic, ROCKE-3D and the UM. This paper, focused on
the simulated observations, is the third part of a trilogy, following the
analysis of two land planet scenarios (part I) and two aquaplanet scenarios
(part II). Here, we show a robust agreement between the simulated spectra and
the number of transits estimated to detect the land planet atmospheres. For the
aquaplanet ones, using atmospheric data from any of the four GCMs would require
at least 17 transits. This prediction corresponds to UM simulated data which
produces the lowest and thinnest clouds. Between 35-40% more clouds are
predicted by ExoCAM or LMD-G due to higher thick terminator clouds. For the
first time this work provides "GCM uncertainty error bars" of 35-40% that need
to be considered in future analyses of transmission spectra. We also analyzed
the inter-transit variability induced by weather patterns and changes of
terminator cloudiness between transits. Its magnitude differs significantly
between the GCMs but its impact on the transmission spectra is within the
measurement uncertainties. THAI has demonstrated the importance of model
intercomparison for exoplanets and also paved the way for a larger project to
develop an intercomparison meta-framework, namely the Climates Using
Interactive Suites of Intercomparisons Nested for Exoplanet Studies (CUISINES).
