FCReplaceD[expr, rule] replaces D in expr according to the supplied replacement rule (e.g. D -> 4 - 2*Epsilon) but doesn’t touch D inside Pairs and DiracGammas, i.e the dimension of scalar products, metric tensors and Dirac matrices is unchanged. The latter can and should be done via ChangeDimension.
Applying the replacement rule directly to the expression doesn’t give the desired result
FCI[D MTD[\[Mu], \[Nu]]]
% /. D -> 4 - 2 EpsilonD g^{\mu \nu }
(4-2 \varepsilon ) g_{\{4-2 \varepsilon ,4-2 \varepsilon \}}{}^{\mu \nu }
With FCReplaceD we get what we want
FCReplaceD[D MTD[\[Mu], \[Nu]], D -> 4 - 2 Epsilon]
ChangeDimension[%, 4](4-2 \varepsilon ) g^{\mu \nu }
(4-2 \varepsilon ) \bar{g}^{\mu \nu }