If the disappearance of the broad emission lines observed in changing-look quasars originates from the obscuration of the quasar core by dusty clouds moving in the torus, high linear optical polarization would be expected in those objects. We then measured the rest-frame UV-blue linear polarization of a sample of 13 changing-look quasars, 7 of them being in a type 1.9-2 state. For all quasars but one the polarization degree is lower than 1%. This suggests that the disappearance of the broad emission lines cannot be attributed to dust obscuration, and supports the scenario in which changes of look are caused by a change in the rate of accretion onto the supermassive black hole. Such low polarization degrees also indicate that these quasars are seen under inclinations close to the system axis. One type 1.9-2 quasar in our sample shows a high polarization degree of 6.8%. While this polarization could be ascribed to obscuration by a moving dusty cloud, we argue that this is unlikely given the very long time needed for a cloud from the torus to eclipse the broad emission line region of that object. We propose that the high polarization is due to the echo of a past bright phase seen in polar-scattered light. This interpretation raises the possibility that broad emission lines observed in the polarized light of some type 2 active galactic nuclei can be echoes of past type 1 phases and not evidence of hidden broad emission line regions. Based on observations made with the William Herschel telescope operated on the island of La Palma by the Isaac Newton Group of Telescopes in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias and observations made with ESO Very Large Telescope at the Paranal Observatory under program ID 101.B-0209.