In this study the method of topological sensitivity (TS) for solving inverse scattering problems, previously supported by a broad set of numerical simulations, is put to test experimentally with the focus on 2D obstacle reconstruction in a thin aluminum plate via elastic waves. To this end, the in-plane measurements of transient elastodynamic waveforms along the edges of the plate are effected in a non-contact fashion by a 3D laser Doppler vibrometer. Using an elastodynamic (time-domain) finite element model as a computational platform, the TS reconstruction maps are obtained and analyzed under varying experimental conditions. The results show significant agreement between the defect geometry and its reconstruction, thus demonstrating the utility of the TS approach as an efficient and robust solution tool for this class of inverse problems. For completeness, the experimental investigation includes a set of parametric studies geared toward exposing the effect of key problem parameters on the quality of obstacle reconstruction such as the (dominant) excitation frequency, the source aperture, and the duration of the temporal record. On the analytical front, it is shown that the use of a suitable temporal windowing function in specifying the L2 cost functional (that underpins the TS formulation) is essential from both theoretical and computational points of view.