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While kinetic helicity is not Galilean invariant locally, it is known (K.Moffatt, Journal of Fluid Mechanics, 35, 117 (1969)) that its spatial integralquantifies the degree of knottedness of vorticity field lines. Being atopological property of the flow, mean kinetic helicity is Galilean invariant.Here, we provide a direct mathematical proof that kinetic helicity is Galileaninvariant when spatially integrated over regions enclosed by vorticitysurfaces, \textit{i.e.}, surfaces of zero vorticity flux. We also discussso-called ``relative'' kinetic helicity, which is Galilean invariant whenintegrated over any region in the flow.

On Galilean Invariance of Mean Kinetic Helicity