We remark on the justification of the basis, and relevant issues, of the topological hydrodynamics (in the sense of the knot-theory interpretation of helicity) of the Galerkin-truncated Euler equations with an `inverse' Helmholtz-Kelvin theorem involving the truncated vorticity `frozen in' the \textit{virtual} velocity $\bm{V}$. The (statistical) topology of the time-reversible systems with the viscous terms of the Navier-Stokes equations modified to balance the external forcing, in such a way that the helicity and energy are dynamically invariant (thus also the virtual frozen-in formulation), are discussed as well with an explicit calculation example in the standard Fourier space. The non-unique $\bm{V}$ for both of these two problems can in principle be incompressible. We also remark on the (fictitious) transport issue of the truncated dynamics, with the transport velocity uniquely determined in general and thus not necessarily compatible with extra conditions, supporting and explaining the recent discovery [Moffatt, H. K. 2014 J. Fluid Mech. {\bf 741}, R3] of the non-existence of the \textit{incompressible} transporter for the single-triad-interaction flows. ; Comment: some typos and grammatical errors corrected; the fictitious transport issue clarified better and Moffatt's recent discovery explained more clearly in Sec. 3.2, with particularly two more equations