What does summary of the model (T-stat and p-values) after Matching using R's “Matching” package indicate?

I am using the GenMatch and Match functions in R's Matching package to balance covariates in an observational study via Genetic Matching. However, the documentation for this package does not describe what the measures for assessing treatment effects are very well (in my opinion): https://cran.r-project.org/web/packages/Matching/Matching.pdf

Using the Summary.Match function on the generated model returns the "estimated causal effect" and the standard error (SE). However it also returns a T-stat value and a p-value, which is not explained in the documentation. These measures seem confusing (to me) because, to my best understanding, the treatment effect is not estimated by a simple t-test in this package (as the matched group includes repeated measures and/or ties, and requires bias correction which is done by the package).

So I am not really sure what to make of this T-stat + p-value, and how to report my findings on treatment effect for an academic paper. Any help will be greatly appreciated

Matching relies on the calculations for the variance derived in Abadie & Imbens (2006). It is an unusual estimator that requires re-matching of the units. A&I demonstrated that the ratio of the effect estimate and this variance is asymptotically standard normal, so the p-value comes from evaluating that ratio (i.e., the t-statistic) in the typical way (i.e., using pnorm()).