  In this work we use cMERA, a continuous tensor network, to find a Gaussian
approximation to the ground state of a $T\bar{T}$-deformed scalar CFT on the
line, to first order in the deformation parameter. The result is used to find
the correction to the correlators of scaling operators of the theory and to the
entanglement entropy of a half-line. From the latter, we discuss the
non-localities induced by the $T\bar{T}$-deformation at short length scales. We
find that the kind of non-locality generated by those terms can be considered
as a mild-one, in the sense that it does not violate the area law of
entanglement. In the context of the conjectured connection between cMERA and
holography, we find that at first insight a finite bulk radius can be defined
in the putative geometric dual description of cMERA. However, the entropy
analysis contradicts the proposal that no geometry can be ascribed to the
region outside this radial cutoff.
