The Vainshtein screening mechanism relies on nonlinear interaction terms
becoming dominant close to a compact source. However, theories displaying this
mechanism are generally understood to be low-energy theories: it is unclear
that operators emerging from UV completion do not interfere with terms inducing
Vainshtein screening. In this work, we find a set of interacting massive
Galileon theories that exhibit Vainshtein screening; examining potential UV
completions of these theories, we determine that the screening does not survive
the extension. We find that neglecting operators when integrating out a heavy
field is non-trivial, and either care must be taken to ensure that omitted
terms are small for the whole domain, or one is forced to work solely with the
UV theory. We also comment on massive deformations of the familiar Wess-Zumino
Galileons.