Mixed matrix membranes (MMMs) containing metal–organic frameworks (MOFs) offer precise molecular sieving owing to the ordered porosity of the MOFs. The poor interfacial adhesion between the polymer matrix and the fillers was bridged by grafting the MOF with poly(N-isopropylacrylamide) (PNIPAM) chains, to become entangled with the membranes’ polymer matrix. This strategy was inspired by the strong adhesion between the cementum of the tooth and the surrounding tissues provided by intermingled collagen fibers. MMMs comprising MOF nanoparticles with similar chemical and morphological properties but having various pore sizes (UiO-66–68-NH2) was prepared. Morphological investigations revealed that membranes with PNIPAM-grafted fillers do not suffer from the formation of pinholes at the filler–matrix interface. The organic solvent nanofiltration (OSN) test showed the increase in the flux and molecular weight cut-off values with increasing MOF aperture size which confirms the key role that internal MOF pores play in the filtration.