Theory time about Jasper’s place in the future episodes and maybe reedemption arc???
I know that the show will probably will go for “Jasper, as gem in charge of the mission, this failure is YOURS and so is the real punishment of it“ and that’s why they wanna find her rather than peridot, who they might think or not that’s dead, but still sounds weird they didn’t even told the rubies to check it, but let’s put that with how carefree the show and they were.
My personal theory is that HomeWorld wanna find Jasper because they think she is trying to revive the rebellion as new leader at earth once again.