  We continue the study of a recently proposed solvable irrelevant deformation
of an AdS$_3$/CFT$_2$ correspondence that leads in the UV to a theory with
Hagedorn spectrum. This can be thought of as a single trace analog of the
$T\bar{T}$-deformation of the dual CFT$_2$. Here we focus on the deformed
worldsheet theory in presence of a conformal boundary. First, we compute the
expectation value of a bulk primary operator on the disc geometry. We give a
closed expression for such observable, from which we obtain the anomalous
conformal dimension induced by the deformation. We compare the result with that
coming from the computation of the 2-point correlation function on the sphere,
finding exact agreement. We perform the computation using different techniques
and making a comparative analysis of different regularization schemes to solve
the logarithmically divergent integrals. This enables us to perform further
consistency checks of our result by computing other observables of the deformed
theory: We compute both the bulk-boundary 2-point and the boundary-boundary
2-point functions and are able to reproduce the anomalous dimensions of both
boundary and bulk operators.
