As a top-factory, the LHC is performing a direct study of top-quark anomalous FCNC couplings, which are, however, correlated closely with the rare B- and K-meson decays. In this paper, we study the effects of anomalous tqZ (with q = u, c) couplings in the rare decays B
s,d
→ μ
+
μ
−, B → X
s
ν
$ \overline \nu $
, B → K
(*)
ν
$ \overline \nu $
, K
+ → π+
ν
$ \overline \nu $
, and K
L
→ π0
ν
$ \overline \nu $
. With the up-to-date experimental bounds on the branching rati...