Thermal neutron scattering laws are important nuclear data for many nuclear science and engineering applications. Validation helps to ensure that a thermal neutron scattering law has a high quality and often employs critical benchmarks as integral experiments. Recently, pulsed-neutron die-away benchmarks have been used as an experiment to validate thermal neutron scattering laws. Herein, we evidence how this alternative integral experiment has a high sensitivity to these nuclear data by performing an uncertainty quantification analysis. The analysis randomly sampled the nuclear model parameters associated with hydrogen bound in light water thermal neutron scattering law and sampled other nuclear data that influenced the experiment’s integral parameter (e.g., elastic scattering, absorption in hydrogen and oxygen) from their respective covariance matrices. The thermal neutron scattering law caused an uncertainty in the integral parameter that reached 2.67%, which exceeds by an order of magnitude the uncertainties induced in commonly used thermal solution critical benchmarks. The validation performed here, although limited due to a poor description of the historical experiment, indicated that the ENDF/B-VIII.0 thermal neutron scattering law well predicted the integral parameter. These results motivate further benchmark and validation efforts using pulsed-neutron die-away experiments.