Scalar-tensor theories with a scalar field coupled to the Gauss-Bonnet
invariant can evade no-hair theorems and allow for non-trivial scalar profiles
around black holes. This coupling is characterized by a length scale $\lambda$,
which, in an effective field theory perspective, sets the threshold below which
deviations from General Relativity become significant. LIGO/VIRGO constraints
indicate $\lambda$ is small, implying supermassive black holes should not
scalarize. However, recent work suggests that scalarization can occur within a
narrow window of masses, allowing supermassive black holes to scalarize, while
leaving LIGO/VIRGO sources unaffected. We explore the impact of this scenario
on the stochastic gravitational wave background recently observed by Pulsar
Timing Arrays. We find that scalarization can alter the characteristic strain
produced by circularly inspiralling SMBH binaries and that current data shows a
marginal preference for a non-zero $\lambda$. However, similar signatures could
arise from astrophysical effects such as orbital eccentricity or environmental
interactions, emphasizing the need for improved modeling and longer
observations to discriminate among the different scenarios.
