  Composite topological structures such as superheavy "quasi-stable strings"
(QSS) and "walls bounded by strings" (WBS) arise in realistic extensions of the
Standard Model of high energy physics. We show that the gravitational radiation
emitted in the early universe by these two unstable structures with a
dimensionless string tension $G\mu\approx 10^{-6}$ is consistent with the
NANOGrav evidence of low frequency gravitational background as well as the
recent LIGO-VIRGO constraints, provided the superheavy strings and monopoles
experience a certain amount of inflation. For the case of walls bounded by
strings, the domain walls arise from the spontaneous breaking of a remnant
discrete gauge symmetry around the electroweak scale. The quasi-stable strings,
on the other hand, arise from a two step breaking of a local gauge symmetry.
The monopoles appear from the first breaking and get connected to strings that
arise from the second breaking. Both composite structures decay by emitting
gravitational waves over a wide frequency range. The Bayes factors for QSS and
WBS relative to the inspiraling supermassive black hole binaries are estimated
to be about 60 and 30 respectively, which are comparable with that of
metastable strings and cosmic superstrings.
