So, we know how the Homeworld rubies were looking for Jasper, right? 

Jasper’s old enough to remember the war on Earth and old enough to be part of the “first generation” of Gems that were created.

In “Too Short to Ride,” Peridot mentioned that Homeworld is running out of resources to make Gems like “they used to,” (i.e. like Jasper).

Before the new ep, I had thought maybe they were hunting Jasper down for her failure in the mission and/or wanted to bring her back for punishment. Possibly even shatter her. 

But that seemed out of character for someone like Yellow Diamond who seems to want to make efficient use of all her resources, including her soldiers. Why would she dispatch a bunch of rubies on a mission to retrieve one soldier? Unless Jasper has some crucial information related to the Cluster, it just seems like lot of effort to retrieve one, ostensibly, replaceable gem. There are not too many other explanations I can come up without stretching the canon a bit.

But “Too Short to Ride” fills in the missing piece.

While Jasper might have failed in her mission, she is a part of a generation of Gems that is fast becoming a dying breed. Homeworld no longer has the luxury of simply disposing of soldiers who fail to meet expectations. If small Gems like peridots are all they can produce these days, then they cannot afford to lose the firepower that Quartz-type soldiers provide. 

So, to sum it up: they are trying to get Jasper back because they literally cannot afford to lose her.