  The non-relativistic Skyrme energy density functional (EDF) based collective
Hamiltonian, that takes into account dynamical correlations related to the
restoration of broken symmetries and fluctuations of quadrupole collective
variables, is applied to quantitatively study the impurity effect of $\Lambda$
hyperon on the collectivity of $^{44}$S. Several Skyrme forces for both the
nucleon-nucleon ($NN$) and $\Lambda$-nucleon ($\Lambda N$) interactions are
used. The influence of pairing strengths on the polarization effect of
$\Lambda$ hyperon is also examined. It is found that although these Skyrme
forces with different pairing strengths give somewhat different low-lying
spectra for $^{44}$S, all of them give similar and generally small size of
$\Lambda$ reduction effect (within 5%) on the collective properties.
