  We compute the holographic entanglement entropy contribution from planar
two-dimensional defects in six-dimensional $\mathcal{N}=(2,0)$ superconformal
field theory, holographically dual to probe M2- and M5-branes in $AdS_7 \times
S^4$. In particular, we test the viability of the universal contribution of the
defect to entanglement entropy as a candidate $C$-function. We find that this
coefficient is not monotonic under defect renormalization group flows triggered
by the vacuum expectation value of a marginal operator. Another candidate
$C$-function, the on-shell action inside the entanglement wedge, monotonically
decreases under the flows we study.
