  We revisit the $\Delta F=2$ transitions in the $K$ and $B_{d,s}$ neutral
meson systems in the context of the minimal Left-Right symmetric model. We take
into account, in addition to up-to-date phenomenological data, the
contributions related to the renormalization of the flavor-changing neutral
Higgs tree-level amplitude. These contributions were neglected in recent
discussions, albeit formally needed in order to obtain a gauge independent
result. Their impact on the minimal LR model is crucial and twofold. First, the
effects are relevant in $B$ meson oscillations, for both CP conserving and CP
violating observables, so that for the first time these imply constraints on
the LR scenario which compete with those of the $K$ sector (plagued by
long-distance uncertainties). Second, they sizably contribute to the indirect
kaon CP violation parameter $\varepsilon$. We discuss the bounds from $B$ and
$K$ mesons in both cases of LR symmetry: generalized parity ($\mathcal P$) and
charge conjugation ($\mathcal C$). In the case of $\mathcal P$, the interplay
between the CP-violation parameters $\varepsilon$ and $\varepsilon'$ leads us
to rule out the regime of very hierarchical bidoublet vacuum expectation values
$v_2/v_1<m_b/m_t\simeq 0.02$. In general, by minimizing the scalar field
contribution up to the limit of the perturbative regime and by definite values
of the relevant CP phases in the charged right-handed currents, we find that a
right-handed gauge boson $W_R$ as light as 3 TeV is allowed at the 95% CL. This
is well within the reach of direct detection at the next LHC run. If not
discovered, within a decade the upgraded LHCb and Super B factories may reach
an indirect sensitivity to a Left-Right scale of 8 TeV.
