So, the memory implant theory is a bust. And yes, if there was a memory implant, Jade would've had a way around it. Might've been a little less painless, but she could've made her forget if that's all it was.
Icing on the Cake
Claire has her reasons for needing to talk to and trust Jade, but she wears her heart on her sleeve, and right now her arm is wrapped around Jade's waist. (figuratively, they're on opposite sides of the booth). Also, Claire! Keep your foot off the booth seat! That's impolite.