  The electronic bands of twisted bilayer graphene (TBLG) with a large-period
moir\'e superlattice fracture to form narrow Bloch minibands that are
spectrally isolated by forbidden energy gaps from remote dispersive bands. When
these gaps are sufficiently large, one can study a band-projected Hamiltonian
that correctly represents the dynamics within the minibands. This inevitably
introduces nontrivial geometrical constraints that arise from the assumed form
of the projection. Here we show that this choice has a profound consequence in
a low-energy experimentally-observable signature which therefore can be used to
tightly constrain the analytic form of the appropriate low-energy theory. We
find that this can be accomplished by a careful analysis of the electron
density produced by backscattering of Bloch waves from an impurity potential
localized on the moir\'e superlattice scale. We provide numerical estimates of
the effect that can guide experimental work to clearly discriminate between
competing models for the low-energy band structure.
