  We study the characteristics of scattering processes at step edges on the
surfaces of Strong Topological Insulators (STI), arising from restrictions
imposed on the $S$-matrix \emph{solely} by time reversal symmetry and
translational invariance along the step edge. We show that the `perfectly
reflecting' step edge that may be defined with these restrictions allow
modulations in the Local Density of States (LDOS) near the step edge to decay
no slower than $1/x$, where $x$ is the distance from the step edge. This is
faster than in 2D Electron Gases (2DEG) --- where the LDOS decays as
$1/\sqrt{x}$ --- and shares the same cause as the suppression of backscattering
in STI surface states. We also calculate the scattering at a delta function
scattering potential and argue that \emph{generic} step edges will produce a
$x^{-3/2}$ decay of LDOS oscillations. Experimental implications are also
discussed.
