We report on Imaging X-ray polarimetry explorer (IXPE) observations of the Be-transient X-ray pulsar LS V +44 17/RX J0440.9+4431 made at two luminosity levels during the giant outburst in January–February 2023. Considering the observed spectral variability and changes in the pulse profiles, the source was likely caught in supercritical and subcritical states with significantly different emission-region geometry, associated with the presence of accretion columns and hot spots, respectively. We focus here on the pulse-phase-resolved polarimetric analysis and find that the observed dependencies of the polarization degree and polarization angle (PA) on the pulse phase are indeed drastically different for the two observations. The observed differences, if interpreted within the framework of the rotating vector model (RVM), imply dramatic variations in the spin axis inclination, the position angle, and the magnetic colatitude by tens of degrees within the space of just a few days. We suggest that the apparent changes in the observed PA phase dependence are predominantly related to the presence of an unpulsed polarized component in addition to the polarized radiation associated with the pulsar itself. We then show that the observed PA phase dependence in both observations can be explained with a single set of RVM parameters defining the pulsar’s geometry. We also suggest that the additional polarized component is likely produced by scattering of the pulsar radiation in the equatorial disk wind.