Origami self-proclaims herself as Shido’s girlfriend or lover, even though Shido doesn’t know about it and it's a one-sided love interest from Origami. Origami uses every chance she gets to make her relationship with Shido much, much closer. Her love for him is quite unhealthy as she often disregards most of Shido's feelings or thoughts and can come off as self-centered.
Put simply, Origami is a stalker, and Shido is the focus of her desires. She has secretly been following Shido around in his everyday life since before the start of the series.
Origami sees Tohka as an enemy, love rival, or just an annoying "baka" that gets in her way with Shido. Origami shows little respect for her as the quarrel between them as Spirit and AST member remains unsettled, despite the fact that Tohka's powers are sealed. Origami still views her as dirty as she views every spirit and seems to want to hurt her by other means since Origami isn't allowed to hurt Tohka herself as long as her powers are sealed.