Ionically crosslinked hydrogels containing metal coordination motifs have piqued the interest of researchers in recent decades due to their self-healing and adhesive properties. In particular, catechol-functionalized bulk hydrogels have received a lot of attention because of their bioinspired nature. By contrast, very little is known about thin viscoelastic membranes made using similar chelator-ion pair motifs. This shortcoming is surprising because the unique interfacial properties of these membranes, namely, their self-healing and adhesion, would be ideal for capsule shells, adhesives, or for drug delivery purposes. We recently demonstrated the feasibility to fabricate 10 nm thick viscoelastic membranes from catechol-functionalized surfactants that are ionically crosslinked at the liquid/liquid interface. However, it is unclear if the vast know-how existing on the influence of the chelator-ion pair on the mechanical properties of ionically crosslinked three-dimensional (3D) hydrogels can be translated to two-dimensional (2D) systems. To address this question, we compare the dynamic mechanical properties of ionically crosslinked pyrogallol functionalized hydrogels with those of viscoelastic membranes that are crosslinked using the same chelator-ion pairs. We demonstrate that the storage and loss moduli of viscoelastic membranes follow a trend similar to that of the hydrogels, with the membrane becoming stronger as the ion-chelator affinity increases. Yet, membranes relax significantly faster than bulk equivalents. These insights enable the targeted design of viscoelastic, adhesive, self-healing membranes possessing tunable mechanical properties. Such capsules can potentially be used, for example, in cosmetics, as granular inks, or with additional work that includes replacing the fluorinated block by a hydrocarbon-based one in drug delivery and food applications.