We have studied the mechanisms of a pulsed laser impact on the magnetization configuration in ferrimagnetic multilayered magnetic nanostructures, specifically, tunneling magnetic junctions taking into account laser-induced kinetic effects. The mechanism of such the laser-induced impact is a complex process of laser-induced thermal demagnetization of magnetic sublattices with subsequent biasing by internal magnetic fields of different nature. Depending on an intensity of laser pulses, it can be effective internal magnetic fields of laser irradiation or internal magnetic fields connected with different rates of the heat demagnetization of ferrimagnetic sublattices. It is shown that investigated ferrimagnetic nanostructures are characterized very small times of the laser-induced remagnetization, which can attain subpicosecond scales.