Dual overlaps and finite coupling 't Hooft loops

Integrable $su(2\mathrm{\mid }2{)}_c$ symmetric models have integrable boundaries with $osp(2\mathrm{\mid }2)$ symmetries, which can be embedded into $su(2\mathrm{\mid }2{)}_c$ in two different ways. We dualize the previously obtained asymptotic overlap formulas for one of the embeddings to describe the other embedding and apply the results to describe the asymptotic expectation values of local operators in the presence of a 't Hooft line in N=4 SYM. A peculiar feature of the setting is that in certain gradings only descendant states have non-vanishing overlaps with the boundary state and the overlap formula is not factorized for the Bethe roots.