The problem of the plane H-polarized electromagnetic wave scattering by flat pre-fractal impedance strips' gratings is examined. For this purpose, a mathematical model in the form of the first kind singular integral equation system is modified for correct usage. Considerable attention is focused on the asymptotic model of the H-polarized electromagnetic wave scattering by sparsely filled grating, which has an explicit solution. The scattered electromagnetic field in the far-zone is considered in details. Dependences of scattering integral characteristics on values of the strip impedance and angles of the plane H-polarized electromagnetic wave incidence upon the grating are studied.