  We analytically compute the scanning tunneling microscopy (STM) signatures of
integer-filled correlated ground states of the magic angle twisted bilayer
graphene (TBG) narrow bands. After experimentally validating the
strong-coupling approach at $\pm 4$ electrons/moir\'e unit cell, we consider
the spatial features of the STM signal for 14 different many-body correlated
states and assess the possibility of Kekul\'e distortion (KD) emerging at the
graphene lattice scale. Remarkably, we find that coupling the two opposite
graphene valleys in the intervalley-coherent (IVC) TBG insulators does not
always result in KD. As an example, we show that the Kramers IVC state and its
nonchiral $\mathrm{U} \left( 4 \right)$ rotations do not exhibit any KD, while
the time-reversal-symmetric IVC state does. Our results, obtained over a large
range of energies and model parameters, show that the STM signal and Chern
number of a state can be used to uniquely determine the nature of the TBG
ground state.
