It seems that the hydrogen bond band (about 3500 cm-1) becomes less intense, so the amino-groups are adsorption centers, probably. Note that MB is a weak acid in the normal state. 

As stated above your hydroxyl band region and in particular the peaks present away from the normal background large peak of adsorbed water (~3500 wavenumber) are gone after adsorption. This suggests sorption onto some hydroxyl like bond space present in your MOF, or particularly the removal of sorbed water and replacement with sorbed MB. As stated MB is a weak acid in the normal state, so it would make sense to begin your search for the sorption site at basic sites present on the MOF, for instance at the amino groups. I would first figure out if those sharp peaks at 3500 correspond to added amine groups onto MIL-125 perhaps by taking spectra before and after NH2 addition (or on a bare MIL-125 MOF and a NH2-MIL-125 MOF) and compare those first, then make the case that sorption of MB is causing the apparent loss of these NH2 peaks. 

Thanks to all of you dear.