I'm wondering whether they will seek to hold the territory, or at some point quickly withdraw back beyond their border to avoid losses?
There is talk about Ukrainians digging trenches on Russian territory, which would indicate that they plan to hold the territory, or at least defend it as much as they can to force high losses on the Russians when they try to take it back.
It would be foolish to just retreat, because retaking fortified territory is extremely costly. Russia is losing a lots of men and equipment in the Donbas for very slow advances, but it gains territory nevertheless. If Ukraine manages to take a big chunk of land in Kursk with very little losses, as it seems it is the case right now, they should quickly fortify it and make it very expensive for the Russians to take it back.
The way the war in the Donbass is going, Ukraine trades land for inflicting higher losses on the Russian side. Getting a big chunk of land inside Russia is extremely useful, as it will allow Ukraine to trade that land for more Russian loses, a land that it aquired rapidly and with very few losses.
I think it would be a big mistake for Ukraine to simply withdraw, and I doubt this will happen.
Also, keep in mind that Russia needs to completely destroy the territory they take back, as their tactics rely in artillery fire and dropping large glide bombs on the defensive positions. While in the Donbas they destroy Ukrainian land, doing the same in Kursk would force them to destroy Russian villages, which will not sit very well with the Russian population.