  We present a quantization of a Lie coideal structure for twisted half-loop
algebras of finite-dimensional simple complex Lie algebras. We obtain algebra
closure relations of twisted Yangians in Drinfeld J presentation for all
symmetric pairs of simple Lie algebras and for simple twisted even half-loop
Lie algebras. We provide the explicit form of the closure relations for twisted
Yangians in Drinfeld J presentation for the ${\mathfrak{sl}}_3$ Lie algebra.
