I have used Tetrabutyl ammonium bromide for the synthesis of benzaimidazole based ionic liquids, after synthesis hole mass convert into solid. We need to remove TBAB from the ILs
Dissolve the solid in Ethyl acetate and wash the organic layer with water to separate TBAB. After water wash dried the organic layer with anhydrous sodium sulfate and evaporate the organic layer under reduced pressure to get pure compound.
I suggest to you using water dilution. If not appropriate then find a solvent like methanol, ethanol etc. to dissolve on of them and separate each from other.
the fist thing that comes to my mind is: do some solubility test on the tetrabutyl amonium salt and if there are a couple in which your salt is soluble and the ionic liquid insoluble use it to do an extraction. if it is not maybe I would like to try an addition of silver nitrite to precipitate silver bromide and to form tetrabutyl amonium nitrate, the resulting salt should have another kow and maybe could be easily separed but is just something that comes to my mind in a first glance.
Before doing it prepare the corresponding TBAnitrate and do the solubility test