In this paper, we study the chemical properties of the stars in the dwarf satellites around the MW-like host galaxies, and explore the possible effects of several baryonic processes, including supernova (SN) feedback, the reionization of the universe and H$_2$ cooling, on them and how current and future observations may put some constraints on these processes. We use a semi-analytical model to generate MW-like galaxies, for which a fiducial model can reproduce the luminosity function and the stellar metallicity--stellar mass correlation of the MW dwarfs. Using the simulated MW-like galaxies, we focus on investigating three metallicity properties of their dwarfs: the stellar metallicity--stellar mass correlation of the dwarf population, and the metal-poor and metal-rich tails of the stellar metallicity distribution in individual dwarfs. We find that (1) the slope of the stellar metallicity--stellar mass correlation is sensitive to the SN feedback strength and the reionization epoch; (2) the extension of the metal-rich tails is mainly sensitive to the SN feedback strength; (3) the extension of the metal-poor tails is mainly sensitive to the reionization epoch; (4) none of the three chemical properties are sensitive to the H$_2$ cooling process; and (5) comparison of our model results with the current observational slope of the stellar metallicity--stellar mass relation suggests that the local universe is reionized earlier than the cosmic average and local sources may have a significant contribution to the reionization in the local region, and an intermediate to strong SN feedback strength is preferred. Future observations of metal-rich and metal-poor tails of stellar metallicity distributions will put further constraints on the SN feedback and the reionization processes.
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