Anomalies in the flux ratios of the images of quadruply-lensed quasars have been used to constrain the nature of dark matter. Assuming these lensing perturbations are caused by dark matter haloes, it is currently possible to constrain the mass of a hypothetical Warm Dark Matter (WDM) particle to be m_χ > 5.2 keV. However, the assumption that perturbations are only caused by DM haloes might not be correct as other structures, such as filaments and pancakes, exist and make up a significant fraction of the mass in the Universe, ranging between 5  |${{\ \rm per\ cent}}$| and 50 |${{\ \rm per\ cent}}$| depending on the dark matter model. Using novel fragmentation-free simulations of 1 and 3 keV WDM cosmologies we study these ‘non-halo’ structures and estimate their impact on flux-ratio observations. We find that these structures display sharp density gradients with short correlation lengths, and can contribute more to the lensing signal than all haloes up to the half-mode mass combined, thus reducing the differences expected among WDM models. We estimate that non-halo structures can be the dominant cause of line-of-sight flux-ratio anomalies in very warm, but already excluded, |$m_x \sim 1 \,\rm {keV}$| scenarios. For colder cases |$m_x \gtrsim 3 \,\rm {keV}$|⁠, we estimate that non-haloes can contribute about |$5 - 10{{\ \rm per\ cent}}$| of the total flux-ratio signal.