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We use the constrained random phase approximation (cRPA) method to calculate the Hubbard $U$ parameter in four one-dimensional magnetic transition metal atom oxides of composition XO$_2$ (X = Mn, Fe, Co, Ni) on Ir(100). In addition to the expected screening of the oxide, i.e., a significant reduction of the $U$ value by the presence of the metal substrate, we find a strong dependence on the electronic configuration (multiplet) of the X($d$) orbital. Each particular electronic configuration attained by atom X is dictated by the O ligands, as well as by the charge transfer and hybridization with the Ir(100) substrate. We find that MnO$_2$ and NiO$_2$ chains exhibit two different screening regimes, while the case of CoO$_2$ is somewhere in between. The electronic structure of the MnO$_2$ chain remains almost unchanged upon adsorption. Therefore, in this regime, the additional screening is predominantly generated by the electrons of the neighboring metal surface atoms. The screening strength for NiO$_2$/Ir(100) is found to depend on the Ni($d$) configuration in the adsorbed state. The case of FeO$_2$ shows an exceptional behavior, as it is the only insulating system in the absence of metallic substrate and, thus, it has the largest $U$ value. However, this value is significantly reduced by the two mentioned screening effects after adsorption.