  We calculate the pole masses of pseudoscalar mesons in a strongly magnetized
medium within the framework of the SU(3) Nambu-Jona--Lasinio model, using a
magnetic field-independent regularization scheme. We employ both a constant and
a magnetic field-dependent coupling $G(B)$, the latter being fitted to
reproduce lattice QCD results for the pseudocritical chiral transition
temperature. Numerical results for the pole masses are obtained for definite
parametrizations of the model. For neutral mesons, the use of $G(B)$ provides
closer agreement with lattice QCD results, which reveal a decrease of the mass
with the external field. On the contrary, charged mesons masses are enhanced by
$B$, showing no sign of the non-monotonous behavior found in recent lattice QCD
simulations.
