CLCD[m, n, r] evaluates to Eps[CartesianIndex[m, D-1], CartesianIndex[n, D-1], CartesianIndex[r,D-1]] applying FeynCalcInternal.
CLC[m,...][p, ...] evaluates to Eps[CartesianIndex[m, D-1], ..., CartesianMomentum[p, D-1], ...] applying FeynCalcInternal.
When some indices of a Levi-Civita-tensor are contracted with 3-vectors, FeynCalc suppresses explicit dummy indices by putting those vectors into the corresponding index slots. For example, \varepsilon^{p_1 p_2 p_3} (accessible via CLCD[][p1,p2,p3]) correspond to \varepsilon^{i j k} p_1^i p_2^j p_3^k.
CLCD[i, j, k]\overset{\text{}}{\epsilon }^{ijk}
CLCD[i, j, k] // FCI // StandardForm
(*Eps[CartesianIndex[i, -1 + D], CartesianIndex[j, -1 + D], CartesianIndex[k, -1 + D]]*)CLCD[i, j][p]\overset{\text{}}{\epsilon }^{ijp}
CLCD[i, j][p] // FCI // StandardForm
(*Eps[CartesianIndex[i, -1 + D], CartesianIndex[j, -1 + D], CartesianMomentum[p, -1 + D]]*)CLCD[i, j][p] CLCD[i, j][q] // Contract // Factor2(2-D) (3-D) (p\cdot q)
CLCD[i, j, k] CVD[Subscript[p, 1], i] CVD[Subscript[p, 2], j] CVD[Subscript[p, 3], k]
Contract[%]
p_1{}^i p_2{}^j p_3{}^k \overset{\text{}}{\epsilon }^{ijk}
\overset{\text{}}{\epsilon }^{p_1p_2p_3}