  Measuring the imprint of primordial gravitational waves in the cosmic
microwave background (CMB) polarisation field is one of the main goals in
modern cosmology. However, the so called $B$-mode polarisation can be generated
by different sources besides the primary one predicted by inflationary
theories, known as secondary $B$-mode signal. Among them, CMB lensing and
astrophysical foregrounds play an important role. Moreover, a partial sky
analysis leads to a leakage between $E$-modes and $B$-modes. In this article,
we use the well known Minkowski functionals (MF) statistics to study the
significance of this leakage in the CMB lensing $B$-mode signal. We find that
the MF can detect the $E$-to-$B$ leakage contamination, thus it should not be
neglected in future CMB data analysis.
