We investigate the transmission and backscattering of solitary waves in granular crystals to assess their initial strains under various levels of compression. We assemble a one-dimensional granular chain that includes a pair of heavy impurities to scatter incident solitary waves. Using a scanning laser Doppler vibrometer and an instrumented sensor particle, we experimentally show that the speed of solitary waves backscattered in the region of impurities is highly sensitive to the applied strains. Based on this pulse-echo mechanism of solitary waves, we briefly demonstrate the feasibility of localized strain sensing via multiple scatterers distributed in a granular chain. We find that numerical results obtained from a discrete element model are in excellent agreement with experimental results. This study forms a foundation for constructing a solitary wave-based sensor system to measure distributed strains in ordered granular systems.