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We investigate the effects of salt concentration on the rheological properties of dipeptide hydrogel fibres at liquid-liquid interfaces. The interfaces were subjected to large amplitude oscillatory dilation (LAOD) experiments across a range of oscillation strains and frequencies. Lissajous plots of pressure-strain were used for characterizing the viscoelastic properties and for identifying apparent yielding. We show that key aspects of the rheological response of the interfaces vary significantly with salt concentration. At low strain, independent of salt concentration, Lissajous curves show an almost elliptical shape. As the strain is increased, asymmetry in Lissajous curves evidences a non-linear response. The departure from an ellipse is most obvious at negative strain (at moderate to high salt concentrations) and is suggestive of strain-hardening on compression. The Lissajous curves tilt towards the diagonal at elevated salt concentration demonstrating that the interfaces are becoming increasingly elastic. However, increasing the frequency of the oscillation has little systematic effect. We infer that the addition of salt leads to the development of structure on the interfaces from our observations strain-hardening and of the increasingly elastic response. To fully capture the range of behaviour, we suggest a modification of the analysis to calculate the strain-hardening ratio S used to quantify the degree of non-linearities from Lissajous figures, so as to better reveal the presence of instant strain-softening and strain-hardening responses.