  The study of $\mathrm{T}\overline{\mathrm{T}}$-perturbed quantum field
theories is an active area of research with deep connections to fundamental
aspects of the scattering theory of integrable quantum field theories,
generalised Gibbs ensembles, and string theory. Many features of these
theories, such as the peculiar behaviour of their ground state energy and the
form of their scattering matrices, have been studied in the literature.
However, so far, very few studies have approached these theories from the
viewpoint of the form factor program. From the perspective of scattering
theory, the effects of a $\mathrm{T}\overline{\mathrm{T}}$ perturbation (and
higher spin versions thereof) is encoded in a universal deformation of the
two-body scattering matrix by a CDD factor. It is then natural to ask how these
perturbations influence the form factor equations and, more generally, the form
factor program. In this paper, we address this question for free theories,
although some of our results extend more generally. We show that the form
factor equations admit general solutions and how these can help us study the
distinct behaviour of correlation functions at short distances in theories
perturbed by irrelevant operators.
