  We study the implications of recent lattice QCD results for the magnetic
field dependence of the quarks dynamical masses on the 't Hooft determinant
extended Nambu--Jona-Lasinio Model in the light and strange quark sectors
(\emph{up}, \emph{down} and \emph{strange}). The parameter space is constrained
at vanishing magnetic field, using the quarks dynamical masses and the meson
spectra, whereas at non-vanishing magnetic field strength the dependence of the
dynamical masses of two of the quark flavors is used to fit a magnetic field
dependence on the model couplings, both the four-fermion Nambu--Jona-Lasinio
interaction and the six-fermion 't Hooft flavor determinant. We found that this
procedure reproduces the inverse magnetic catalysis, and the strength of the
scalar coupling decreases with the magnetic field, while the strength of the
six-fermion 't Hooft flavor determinant increases with the magnetic field.
