We provide a refined and much more simplified Einstein-Gauss-Bonnet inflationary theoretical framework, which is compatible with the GW170817 observational constraints on the gravitational wave speed. As in previous works, the constraint that the gravitational wave speed is $c_T^2=1$ in natural units, results to a constraint differential equation that relates the coupling function of the scalar field to the Gauss-Bonnet invariant $xi(phi)$ and the scalar potential $V(phi)$. Adopting the slow-roll conditions for the scalar field and the Hubble rate, and in contrast to previous works, by further assuming that $kappa frac{xi }{xi}ll 1$, which is motivated by slow-roll arguments, we succeed in providing much more simpler expressions for the slow-roll indices and for the tensor and scalar spectral indices and for the tensor-to-scalar ratio. We exemplify our refined theoretical framework by using an illustrative example with a simple power-law scalar coupling function $xi(phi)sim phi^{ u}$ and as we demonstrate the resulting inflationary phenomenology is compatible with the latest Planck data. Moreover, this particular model produces a blue-tilted tensor spectral index, so we discuss in brief the perspective of describing the NANOGrav result with this model as is indicated in the recent literature.
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