Proposition: Residual readout does not retract the return

For the declared residual factor,

including all surviving receiver factors and references. Thus unreported residual readout followed by forgetting leaves the already returned accessible channel unchanged. The same holds for every unreported local CPTP residual operation.

Proof. For $X={\sum }_{i,j}{X}_{ij}\otimes |i⟩⟨j{|}_B$, both operations return ${\sum }_i{X}_{ii}$. The general statement follows because the local adjoint preserves $I_B$.