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Cosmic rays interacting with the Milky Way circumgalactic gas produce high energy neutrinos and photons observable at the Earth. This must contribute to the (10...1000) TeV band Ice Cube neutrino spectrum. However, previous studies reported very different estimates of this contribution, so it was unclear whether it is essential. Here we readdress the calculation of this circumgalactic neutrino flux under various assumptions. We find this contribution to be subleading provided gamma-ray constraints are satisfied