We introduce a minimalistic presentation for the twisted Yangians \({}^\imath \mathscr {Y}\) associated with split symmetric pairs (or Satake diagrams) introduced in Lu et al. (Commun Math Phys 406:98, 2025) via a Drinfeld type presentation. As applications, we establish an injective algebra homomorphism from \({}^\imath \mathscr {Y}\) to the Yangian \(\mathscr {Y}\) , thereby identifying \({}^\imath \mathscr {Y}\) as a right coideal subalgebra of \(\mathscr {Y}\) and proving its isomorphism with the twisted Yangian in the J presentation. Furthermore, we provide estimates for the Drinfeld generators of \({}^\imath \mathscr {Y}\) and describe their images under the coproduct in terms of the Drinfeld generators of \(\mathscr {Y}\) under this identification.
