  We study perturbative renormalization of the composite operators in the
$T\bar T$-deformed two-dimensional free field theories. The pattern of
renormalization for the stress-energy tensor is different in the massive and
massless cases. While in the latter case the canonical stress tensor is not
renormalized up to high order in the perturbative expansion, in the massive
theory there are induced counterterms at linear order. For a massless theory
our results match the general formula derived recently in [1].
