Recent gravitational wave observations allow us to probe gravity in the strong and dynamical field regime. In this paper, we focus on testing Einstein-dilation Gauss-Bonnet gravity which is motivated by string theory. In particular, we use two new neutron star black hole binaries (GW200105 and GW200115). We also consider GW190814 which is consistent with both a binary black hole and a neutron star black hole binary. Adopting the leading post-Newtonian correction and carrying out a Bayesian

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... v-chain Monte Carlo analyses, we derive the 90% credible upper bound on the coupling constant of the theory as √(α_GB)≲ 1.33 km, whose consistency is checked with an independent Fisher analysis. This bound is stronger than the bound obtained in previous literature by combining selected binary black hole events in GWTC-1 and GWTC-2 catalogs. We also derive a combined bound of √(α_GB)≲ 1.18 km by stacking GW200105, GW200115, GW190814, and selected binary black hole events. In order to check the validity of the effect of higher post-Newtonian terms, we derive corrections to the waveform phase up to second post Newtonian order by mapping results in scalar-tensor theories to Einstein-dilation Gauss-Bonnet gravity. We find that such higher-order terms improve the bounds by 14.5% for GW200105 and 6.9% for GW200115 respectively.