  We present a catalog of stellar companions to host stars of Transiting
Exoplanet Survey Satellite Objects of Interest (TOIs) identified from a
marginalized likelihood ratio test that incorporates astrometric data from the
Gaia Early Data Release 3 catalog (EDR3). The likelihood ratio is computed
using a probabilistic model that incorporates parallax and proper-motion
covariances and marginalizes the distances and 3D velocities of stars in order
to identify comoving stellar pairs. We find 172 comoving companions to 170
non-false-positive TOI hosts, consisting of 168 systems with two stars and 2
systems with three stars. Among the 170 TOI hosts, 54 harbor confirmed planets
that span a wide range of system architectures. We conduct an investigation of
the mutual inclinations between the stellar companion and planetary orbits
using Gaia EDR3, which is possible because transiting exoplanets must orbit
within the line of sight; thus, stellar companion kinematics can constrain
mutual inclinations. While the statistical significance of the current sample
is weak, we find that 73$^{+14}_{-20}\%$ of systems with Kepler-like
architectures ($R_{P}$ $\leq$ 4 $R_\oplus$ and $a$ $<$ 1 AU) appear to favor a
nonisotropic orientation between the planetary and companion orbits with a
typical mutual inclination $\alpha$ of 35 $\pm$ 24$^\circ$. In contrast,
65$^{+20}_{-35}\%$ of systems with close-in giants ($P$ $<$ 10 days and $R_{P}$
$>$ 4 $R_{\oplus}$) favor a perpendicular geometry ($\alpha =$ 89 $\pm$
21$^\circ$) between the planet and companion. Moreover, the close-in giants
with large stellar obliquities (planet-host misalignment) are also those that
favor significant planet-companion misalignment.
