...wait, what does that mean?
In the US, a court case originally brought in state court can be removed to federal court if there is a substantial federal issue (an issue under federal law) at stake in the case. State courts can decide federal law, but the defendant (who didn't choose the forum of the case) generally has a right to have federal issues decided in federal court so can seek removal in the early stages of the case. If removed, all federal issues would be decided in federal court, and any remaining state law issues are remanded to state court. A defendant can file for removal to federal court at pretty much any time, and the entire proceeding has to be stopped in state court until the federal court has ruled as to whether it has jurisdiction. If the federal court has jurisdiction, it has to take the case; if it doesn't (because, among other possible reasons, there is no substantial federal issue), it has to remand the case back to state court.
The challenge to the districts is based purely on state law, the North Carolina Constitution. However, the NCGOP is making two arguments here for removal.
The first is that the at least some of the districts sought to be changed were drawn on the order of a federal court (though not by a federal court) in order to ensure compliance with federal law (the VRA) and the federal Constitution, and then they hand-wave to suggest that changing those districts at all would be potentially contrary to or somehow in conflict with federal law, or at least involve interests that could be contrary to federal law (even though it obviously wouldn't be) and therefore they have a right to have a federal court to hear the case. This argument is obvious bunk, and the federal courts will see right through it.
The second argument is truly ridiculous; they claim that any redraw of the map would violate an ostensible federal constitutional right of Republican voters to have representation in Republican-favoring gerrymandered districts. This is even more obvious bunk, and the federal courts will laugh it back to state court.
So it's mostly just a time-wasting procedural tactic in this particular instance. Presumably they are trying to run out the clock on having to redraw before the 2020 elections.