Non-linear mechanical responses observed in networks of many biopolymers such as pectin are important for their functioning as biological systems. Additionally, pectins derived from plant sources are also used for several food and biomedical applications. In the present work, the possible contributions of egg-box bundles in the large deformation response of calcium crosslinked gels of low methoxy pectin are explored using large amplitude oscillatory shear (LAOS). The gels exhibit a significant overshoot in the loss modulus (G′′) and intra-cycle strain-stiffening, more prominent at greater extents of egg-box bundling. This observation signifies the dissipation characteristics of the egg-box bundles in pectin gels, hitherto not reported. The observed non-linear signatures diminish when the extent of bundling as well as the bundle radius decreases below a critical value. We identify different pectin/Ca concentration regimes based on the semi-flexible/flexible nature of the gel network and the non-linear signatures. Monovalent salt addition prior to crosslinking is shown to modify the extent of bundling, thereby influencing the magnitude of G′′ overshoot and strain-stiffening. The intensity of the G′′ overshoot and the extent of strain-stiffening are correlated with the radius of the egg-box bundles obtained from small angle neutron scattering (SANS) data. However, analysis using strain-stiffening models indicates the possible contributions from the semi-flexible nature of egg-box bundles and single chains.