  Radiative corrections in the electroweak sector constitute an essential
component in the ability to disentangle Beyond Standard Model physics from
experimental data. This is particularly relevant for strongly bound systems
undergoing weak decays such as nuclear $\beta$ decay, where its contribution to
top-row CKM unitarity tests is essential. In this Letter we note the need for
an additional radiative correction to the Gamow-Teller form factor in allowed
decays. It concerns a combination of electrostatic final state interactions and
QCD-induced currents. We review the basic derivation and report analytical
results. Due to differences in their theoretical treatment in the literature,
effects on the neutron and mirror systems are distinct. Significant
consequences appear for a comparison of the former with lattice QCD, while
changes occur in the $|V_{ud}|$ extraction in the latter. We discuss new limits
on right-handed currents and provide a new value for $|V_{ud}|$ from mirror
decays.
