  One of the main goals of modern cosmology is to search for primordial
gravitational waves by looking on their imprints in the B-type polarization in
the cosmic microwave background radiation. However, this signal is contaminated
by various sources, including cosmic weak lensing, foreground radiations,
instrumental noises, as well as the E-to-B leakage caused by the partial sky
surveys, which should be well understood to avoid the misinterpretation of the
observed data. In this paper, we adopt the E/B decomposition method suggested
by Smith in 2006, and study the imprints of E-to-B leakage residuals in the
constructed B-type polarization maps, $\mathcal{B}(\hat{n})$, by employing
various statistical tools. We find that the effects of E-to-B leakage are
negligible for the $\mathcal{B}$-mode power spectrum, as well as the skewness
and kurtosis analyses of $\mathcal{B}$-maps. However, if employing the
morphological statistical tools, including Minkowski functionals and/or Betti
numbers, we find the effect of leakage can be detected at very high confidence
level, which shows that in the morphological analysis, the leakage can play a
significant role as a contaminant for measuring the primordial B-mode signal
and must be taken into account for a correct explanation of the data.
