  The Planck mission detected a positive correlation between the intensity
($T$) and $B$-mode polarization of the Galactic thermal dust emission. The $TB$
correlation is a parity-odd signal, whose statistical mean vanishes in models
with mirror symmetry. Recent work has shown with strong evidence that local
handedness of the misalignment between the dust filaments and the sky-projected
magnetic field produces $TB$ signals. However, it remains unclear whether the
observed global $TB$ signal is caused by statistical fluctuations of magnetic
misalignment angles, or whether some parity-violating physics in the
interstellar medium sets a preferred misalignment handedness. The present work
aims to make a quantitative statement about how confidently the
statistical-fluctuation interpretation is ruled out by filament-based
simulations of polarized dust emission. We use the publicly available
DUSTFILAMENTS code to simulate the dust emission from filaments whose magnetic
misalignment angles are symmetrically randomized, and construct the probability
density function of $\xi_{p}$, a weighted sum of $TB$ power spectrum. We find
that Planck data has a $\gtrsim 10\sigma$ tension with the simulated $\xi_{p}$
distribution. Our results strongly support that the Galactic filament
misalignment has a preferred handedness, whose physical origin is yet to be
identified.
