We consider systems of D6-branes in the presence of a non-zero B-field of different ranks. We study the scattering of gravitons in the corresponding supergravity backgrounds. We show that the non-zero B-field does not modify the form of the scattering potential. The graviton scattering equation has two solutions one normalizable and one non normalizable. The normalizable solution does not lead to an absorption, however the non-normalizable one does. We analyse the absorption of gravitons by the branes. We show that in the decoupling limit the graviton flux near the branes is zero, but the absorption is not. This result suggests that even in the presence of a B-field the D6-branes worldvolume theory does not decouple from the bulk gravity. For comparison we analyse the form of the scattering potential and absorption for Dp-branes with p < 5 and for NS5-branes.