  Bursty star formation in dwarf galaxies can slowly transform a steep dark
matter cusp into a constant density core. We explore the possibility that
globular clusters (GCs) retain a dynamical memory of this transformation. To
test this, we use the nbody6df code to simulate the dynamical evolution of GCs,
including stellar evolution, orbiting in static and time-varying potentials for
a Hubble time. We find that GCs orbiting within a cored dark matter halo, or
within a halo that has undergone a cusp-core transformation, grow to a size
that is substantially larger ($R_{\rm eff} > 10$ pc) than those in a static
cusped dark matter halo. They also produce much less tidal debris. We find that
the cleanest signal of an historic cusp-core transformation is the presence of
large GCs with tidal debris. However, the effect is small and will be
challenging to observe in real galaxies. Finally, we qualitatively compare our
simulated GCs with the observed GC populations in the Fornax, NGC 6822, IKN and
Sagittarius dwarf galaxies. We find that the GCs in these dwarf galaxies are
systematically larger ($\langle R_{\rm eff}\rangle \simeq 7.8$ pc), and have
substantially more scatter in their sizes, than in-situ metal rich GCs in the
Milky Way and young massive star clusters forming in M83 ($\langle R_{\rm eff}
\rangle \simeq 2.5$ pc). We show that the size, scatter and survival of GCs in
dwarf galaxies are all consistent with them having evolved in a constant
density core, or a potential that has undergone a cusp-core transformation, but
not in a dark matter cusp.
