We propose a closed formula for the tree-level one-point functions of non-protected operators belonging to an SU(3) sub-sector of the defect CFT dual to the D3–D5 probe brane system with background gauge field flux, k, valid for k=2. The formula passes a number of non-trivial analytical and numerical tests. Our proposal is based on expressing the one-point functions as an overlap between a Bethe eigenstate of the SU(3) spin chain and a certain matrix product state, deriving various factorization properties of the Gaudin norm and performing explicit computations for shorter spin chains. As its SU(2) counterpart, the one-point function formula for the SU(3) sub-sector is of determinant type. We discuss the differences with the SU(2) case and the challenges in extending the present formula beyond k=2.