  Low-mass population III (PopIII) stars of $\lesssim 0.8 M_{\odot}$ could
survive up until the present. Non-detection of low-mass PopIII stars in our
Galaxy has already put a stringent constraint on the initial mass function
(IMF) of PopIII stars, suggesting that PopIII stars have a top-heavy IMF. On
the other hand, some claims that the lack of such stars stems from metal
enrichment of their surface by accretion of heavy elements from interstellar
medium (ISM). We investigate effects of the stellar wind on the metal accretion
onto low-mass PopIII stars because accretion of the local ISM onto the Sun is
prevented by the solar wind even for neutrals. The stellar wind and radiation
of low-mass PopIII stars are modeled based on knowledge of nearby low-mass
stellar systems including our Sun. We find that low-mass PopIII stars traveling
across the Galaxy forms the stellar magnetosphere in most of their life. Once
the magnetosphere is formed, most of neutral interstellar particles are
photoionized before reaching to the stellar surface and are blown away by the
wind. Especially, the accretion abundance of iron will be reduced by a factor
of $< 10^{-12}$ compared with Bondi-Hoyle-Lyttleton accretion. The metal
accretion can enhance iron abundance [Fe/H] only up to $\sim -14$. This
demonstrates that low-mass PopIII stars remain pristine and will be found as
metal free stars and that further searches for them are valuable to constrain
the IMF of PopIII stars.
