  We generalize earlier results on one-point functions in N = 4 SYM with a
co-dimension one defect, dual to the D3-D5-brane setup in type IIB string
theory on AdS5xS5, to a similar setup in the $\beta$-deformed version of the
theory. The treelevel vacuum expectation values of single-trace operators in
the two-scalar-subsector are expressed as overlaps between a matrix product
state (MPS) and Bethe states in the corresponding twisted spin-chain picture.
We comment on the properties of this MPS and present the simplest analytical
overlaps and their behavior in a certain limit (of large k). Importantly, we
note that the deformation alters earlier interpretations of the MPS as an
integrable boundary state, seemingly obstructing simplifications of the
overlaps analogous to the compact determinant formula found in the non-deformed
theory. The results are supplemented with some supporting numerical results for
operators of length eight with four excitations.
