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Recent work uncovered features in the phase space of the Milky Way's stellar halo which may be attributed to the last major merger. When stellar material from a satellite is accreted onto its host, it phase mixes and appears finely substructured in phase space. For a high-eccentricity merger, this substructure most clearly manifests as numerous wrapping chevrons in $(v_r, r)$ space, corresponding to stripes in $(E, θ_r)$ space. We introduce the idea of using this substructure as an alternative subhalo detector to cold stellar streams. We simulate an N-body merger akin to the GSE and assess the impact of subhaloes on these chevrons. We examine how their deformation depends on the mass, pericentre, and number of subhaloes. To quantify the impact of perturbers, we utilise the appearance of chevrons in $(E, θ_r)$ space to introduce a new quantity -- the ironing parameter. We show that: (1) a single flyby of a massive ($\sim 10^{10}$ M$_{\odot}$) subhalo with pericentre comparable to, or within, the shell's apocentre smooths out the substructure, (2) a single flyby of a low mass ($\lesssim 10^8$ M$_{\odot}$) has negligible effect, (3) multiple flybys of subhalos derived from a subhalo mass function between $10^7-10^{10}$ M$_{\odot}$ cause significant damage if deep within the potential, (4) the effects of known perturbers (e.g. Sagittarius) should be detectable and offer constraints on their initial mass. The sensitivity to the populations of subhaloes suggests that we should be able to place an upper limit on the Milky Way's subhalo mass function.