Did Zhen Xuan pass the jade Rao to the palace after her marriage?

Yes She is the blessing of the sovereign, and it is a etiquette and a rule for a maid to appear in court.

For example, one day when the emperor was seriously ill and his health improved slightly, he saw Yu Rao playing with Yuan Che and Hongyan in the imperial garden. Seeing that their two children looked more and more alike, he became suspicious and doubted whether Hongyan was Liu Yun's son, so he became seriously ill.