  JT gravity has a first-order formulation as a two-dimensional BF theory,
which can be viewed as the dimensional reduction of the Chern-Simons
description of $3d$ gravity. We consider $T\bar{T}$-type deformations of the
$(0+1)$-dimensional dual to this $2d$ BF theory and interpret the deformation
as a modification of the BF theory boundary conditions. The fundamental
observables in this deformed BF theory, and in its $3d$ Chern-Simons lift, are
Wilson lines and loops. In the $3d$ Chern-Simons setting, we study
modifications to correlators involving boundary-anchored Wilson lines which are
induced by a $T\bar{T}$ deformation on the $2d$ boundary; results are presented
at both the classical level (using modified boundary conditions) and the
quantum-mechanical level (using conformal perturbation theory). Finally, we
calculate the analogous deformed Wilson line correlators in $2d$ BF theory
below the Hagedorn temperature where the principal series dominates over the
discrete series.
