  We investigate the screening masses of neutral pions and sigma mesons in hot
and magnetized quark matter in the framework of a two-flavor lattice-improved
Nambu-Jona-Lasinio (NJL) model with a magnetic field dependent coupling
constant, which is determined by utilizing the results from lattice QCD
simulations. Since such model can well reproduce inverse magnetic catalysis
(IMC), by comparing with the standard NJL model, we systemically analyze the
impacts of IMC on the temperature and magnetic field dependences of the
longitudinal and transverse screening masses of the chiral partners, i.e.
{\pi}^0 and {\sigma} mesons, as well as the screening mass differences between
them. Particularly, it is found that the eB dependences of two alternative
(pseudo)critical temperatures for the chiral transition defined by
{\sigma}-{\pi}^0 meson screening mass differences are consistent with that
defined by the quark condensate.
