  We discuss how to perform consistent extractions of anomalous triple gauge
couplings (aTGC) from electroweak boson pair production at the LHC in the
Standard Model Effective Field Theory (SMEFT). After recasting recent ATLAS and
CMS searches in $pp\to WZ (WW) \to \ell' \nu \ell^+\ell^- (\nu_{\ell})$
channels, we find that: (a) working consistently at order $\Lambda^{-2}$ in the
SMEFT expansion the existing aTGC bounds from Higgs and LEP-2 data are not
improved, (b) the strong limits quoted by the experimental collaboration are
due to the partial $\Lambda^{-4}$ corrections (dimension-6 squared
contributions). Using helicity selection rule arguments we are able to explain
the suppression in some of the interference terms, and discuss conditions on
New Physics (NP) models that can benefit from such LHC analyses. Furthermore,
standard analyses assume implicitly a quite large NP scale, an assumption that
can be relaxed by imposing cuts on the underlying scale of the process
($\sqrt{\hat{s}}$). In practice, we find almost no correlation between
$\sqrt{\hat{s}}$ and the experimentally accessible quantities, which
complicates the SMEFT interpretation. Nevertheless, we provide a method to set
(conservative) aTGC bounds in this situation, and recast the present searches
accordingly. Finally, we introduce a simple NP model for aTGC to compare the
bounds obtained directly in the model with those from the SMEFT analysis.
