In this work, we propose refinements to the difference-smoothing algorithm for measurement of time delay from the light curves of the images of a gravitationally lensed quasar. The refinements mainly consist of a more pragmatic approach to choose the smoothing time-scale free parameter, generation of more realistic synthetic light curves for estimation of time delay uncertainty and using a plot of normalized $chi^2$ computed over a wide range of trial time delay values to assess the reliability of a measured time delay and also for identifying instances of catastrophic failure. We rigorously tested the difference-smoothing algorithm on a large sample of more than thousand pairs of simulated light curves having known true time delays between them from the two most difficult `rungs -- rung3 and rung4 -- of the first edition of Strong Lens Time Delay Challenge (TDC1) and found an inherent tendency of the algorithm to measure the magnitude of time delay to be higher than the true value of time delay. However, we find that this systematic bias is eliminated by applying a correction to each measured time delay according to the magnitude and sign of the systematic error inferred by applying the time delay estimator on synthetic light curves simulating the measured time delay. Following these refinements, the TDC performance metrics for the difference-smoothing algorithm are found to be competitive with those of the best performing submissions of TDC1 for both the tested `rungs. The MATLAB codes used in this work and the detailed results are made publicly available at https://github.com/rathnakumars/difference-smoothing
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