  The combination of non-minimal couplings to gravity with the
post-inflationary kinetic-dominated era typically appearing in quintessential
inflation scenarios may lead to the spontaneous symmetry breaking of internal
symmetries and its eventual restoration at the onset of radiation domination.
On general grounds, the breaking of these symmetries leads to the generation of
short-lived topological defects that tend to produce gravitational waves until
the symmetry is restored. We study here the background of gravitational waves
generated by a global cosmic string network following the dynamical symmetry
breaking and restoration of a $U(1)$ symmetry. The resulting power spectrum
depends on the duration of the heating process and it is potentially
detectable, providing a test on the existence of non-minimal couplings to
gravity and the characteristic energy scale of post-inflationary physics.
