  We describe the effect of the marginal deformation of the $\cal N = (4, 4)$
superconformal $(T^4)^N /S_N$ orbifold theory on a doublet of R-neutral twisted
Ramond fields, in the large-$N$ approximation. Our analysis of their dynamics
explores the explicit analytic form of the genus-zero four-point function
involving two R-neutral Ramond fields and two deformation operators. We compute
this correlation function with two different approaches: the Lunin-Mathur
path-integral technique and the stress-tensor method. From its short distance
limits, we extract the OPE structure constants and the scaling dimensions of
non-BPS fields appearing in the fusion. In the deformed CFT, at second order in
the deformation parameter, the two-point function of the $n$-twisted Ramond
fields is UV-divergent. We perform an appropriate regularization, together with
a renormalization of the undeformed fields, obtaining finite, well-defined
corrections to their two-point functions and their bare conformal weights, for
$n < N$. The fields with maximal twist $n=N$ remain protected from
renormalization, with vanishing anomalous dimensions.
