Being the ace of the AST team, Ryouko has acknowledge Origami's skills as being one of the best in her squad. However, she often scolds Origami for risking her life too much during their battles with the Spirits, often questioning if Origami wants to die an earlier death. However, there is a degree of trust between the two, as Ryouko told Origami about the whereabouts of the White Licorice in order to allow her to protect Shido from Jessica Bailey's attack.
As the Origami's personality in the new timeline was vastly different, it can be assumed that their relationship was similarly very different.
After Origami left the AST, the two still kept in touch, since Origami was able to contact her when Kotori told her to find friends to buy their doujin. While she questioned the appearance of the other Spirits, she eventually dropped the matter when Origami told her it was just a coincidence.