  We study the phase diagram for strongly interacting matter using the 't Hooft
determinant extended Nambu--Jona-Lasinio model with a Polyakov loop in the
light and strange quark sectors (\emph{up}, \emph{down} and \emph{strange})
focusing on the effect of a magnetic field dependence of the coupling strengths
of these interactions. This dependence was obtained so as to reproduce recent
lattice QCD results for the magnetic field dependence of the quarks dynamical
masses.
  A finite magnetic field is known to induce several additional first-order
phase transition lines with the respective Critical End Points (CEP) in the
temperature-quark chemical potential phase diagram when compared to the zero
magnetic field case. A study of the magnetic field dependence in the range
$eB=0-0.6~\mathrm{GeV}^2$ of the location of these CEPs reveals that the
initial one as well as several of the new ones only survive up to a critical
magnetic field. Only two remain in the upper limit of the studied magnetic
field strength. A comparison of the results obtained with versions of the model
with and without Polyakov loop is also done.
  We also found that the inclusion of the magnetic field dependence on the
coupling strengths, while not changing the qualitative features of the phase
diagram, affects the location of these CEPs. The comparison of results with and
without a regularization cutoff in the medium part of the integrals does not
show a significant change.
