  We reconsider the two-point string scattering amplitudes of massless
Neveu-Schwarz--Neveu-Schwarz states of Type IIB orientifold superstring theory
on the disk and projective plane in ten dimensions and analyse its $\alpha'$
expansion. We also discuss the unoriented Type IIB theory on
$T^6/\mathbb{Z}_2\times\mathbb{Z}_2$ where two-point string scattering
amplitudes of the complex K\"ahler moduli and complex structures of the
untwisted sector are computed on the disk and projective plane. New results are
obtained together with known ones. Finally, we compare string scattering
amplitudes results at $\alpha'^2$-order with the (curvature)$^2$ terms in the
low energy effective action of D-branes and $\Omega$-planes in both cases.
