  We study the entanglement entropy of free fermions in 2d in the presence of a
partially transmitting interface that splits Minkowski space into two
half-spaces. We focus on the case of a single interval that straddles the
defect, and compute its entanglement entropy in three limits: Perturbing away
from the fully transmitting and fully reflecting cases, and perturbing in the
amount of asymmetry of the interval about the defect. Using these results
within the setup of the Poincar\'e patch of AdS$_2$ statically coupled to a
zero temperature flat space bath, we calculate the effect of a partially
transmitting AdS$_2$ boundary on the location of the entanglement island
region. The partially transmitting boundary is a toy model for black hole
graybody factors. Our results indicate that the entanglement island region
behaves in a monotonic fashion as a function of the transmission/reflection
coefficient at the interface.
