Horizon-redshift transfer in black-hole direct-wave damping

Direct waves from black-hole mergers may probe horizon dynamics, but their observed envelopes need not decay at the Kerr surface-gravity rate. We compute the complex-frequency spin-$-2$, $\ell=m=2$ Teukolsky response driven by a redshift-stretched near-horizon source. Through Kerr screening and source convolution, the calculation maps the local surface-gravity scale $\kappa$ into the finite-window envelope damping $\gamma_{\rm eff}$ measured at infinity. For GW250114, this calculation gives $\gamma_{\rm eff}/\kappa\simeq0.6$, or $\gamma_{\rm eff}\simeq0.4~{\rm ms}^{-1}$, consistent with QNM-subtracted residuals and a joint H1--L1 residual analysis. An instantaneous-source control recovers the impulse-response damping near $\kappa$, whereas finite-duration plunge-source, test-particle and radial-normalized source realizations give $\gamma_{\rm eff}<\kappa$. A residual-level check in GW231226 favours the same finite-window damping prediction. These results identify direct-wave envelope damping as a horizon-redshift transfer observable rather than a direct measurement of surface gravity.