  We study theoretically by a quantum-mechanical approach the general
scattering problem of a straight step defect on the surface of topological
insulator $\mathrm{Bi}_{2}\mathrm{Te}_{3}$ with strong warping effect. At high
energy where the warping effect is large, an incident electron on a step defect
running along $\Gamma-\mathrm{M}$ direction may exhibit perfect transmission
whereas on a defect running along $\Gamma-\mathrm{K}$ direction has a finite
probability to be reflected and may even exhibit resonant total reflection.
Transmission properties in the latter case are also very sensitive to whether
there is particle-hole symmetry. The predicted Friedel oscillations and the
power-law decaying behavior of the local density of states (LDOS) near the
defect are in good agreement with recent scanning tunneling microscope
experiments on $\mathrm{Bi}_{2}\mathrm{Te}_{3}$. The high-energy LDOS of the
surface states is also found to show the multi-periodic Friedel oscillations,
caused by competing characteristic scattering processes.
