  We study the correlation functions of local operators in unitary
$\textrm{T}\bar{\textrm{T}}$-deformed field theories defined on a torus, using
their formulation in terms of Jackiw-Teitelboim gravity. We focus on the
two-point correlation function in momentum space when the undeformed theory is
a conformal field theory. The large momentum behavior of the correlation
function is computed and compared to that of
$\textrm{T}\bar{\textrm{T}}$-deformed field theories defined on a plane. For
the latter, the behavior found was $|q|^{-\frac{tq^2}{\pi}}$, where $q$ is the
momentum and $t$ is the deformation parameter. For a torus, the same behavior
is found for $|q|<<L/t$, where $L$ is the torus' length scale. However, for
$|q|>>L/t$, a different behavior is found: $\left(\frac{4\sqrt{t}^5q^2}{\pi e
L^3|T|^2}\right)^{\frac{tq^2}{\pi}}$, where $T$ is the modular parameter of the
torus. Hence, at large momentum, the correlator decays and then grows. This
behavior suggests that operators carrying momentum $q$ are smeared on a
distance scale $t|q|$. The difference from the plane's result illustrates the
non-locality of the theory and the UV-IR mixing.
