  We introduce a skew analogue of the composition of the Cherednik and Drinfeld
functors for twisted Yangians. Our definition is based on the skew Howe
duality, and originates from the centralizer construction of twisted Yangians
due to Olshanski. Using our functor, we establish a correspondence between
intertwining operators on the tensor products of certain modules over twisted
Yangians, and the extremal cocycle on the hyperoctahedral group.
