All quasars vary in their optical flux on a time-scale of years, and it has been proposed that these variations are principally due to gravitational lensing by a cosmologically distributed population of planetary mass objects. This interpretation has implications for the observable properties of gamma-ray bursts (GRBs) -- as a source expands across the nano-arcsecond caustic network, variability is expected -- and data on GRBs can be used to test the proposed model of quasar variability. Here we employ an ultra-relativistic blast-wave model of the source, with no intrinsic variations, to study the effects of nanolensing on GRBs. Taken in isolation the light-curves of the caustic crossings are predictable, and we find that a subset of the predicted light-curves (the image-annihilating fold crossings) resemble the ``pulses'' which are commonly seen in long GRBs. Furthermore, for sources at high redshift the expected time between caustic crossings is of order seconds, comparable to the observed time between pulses. These points suggest that it might be possible to model some of the observed variations of GRBs in terms of nanolensing; however, our simulated light-curves exhibit a small depth of modulation compared to what is observed. This means that the GRB data do not significantly constrain the quasar nanolensing model; it also means that the simplest nanolensing model cannot explain the observed GRB ``pulses''. Viable nanolensing models for pulses probably require a large external beam shear. If a viable model can be constructed it would effect a considerable simplification in source modelling and, ironically, it would explain why no macro-lensed GRBs have been identified to date. (Abridged) ; Comment: 28 pages, 12 figures, matches version accepted by ApJ (fixed minor error in fold lens mapping)