Admittedly, don't know the ins and outs of baggage system, but I don't think it needs to be physically re-tagged - IIRC, I think that's just a visual indicator for bag handlers. I believe it can be changed in the system, to where scanning the bag will indicate where it is supposed to go, including the updated info. that it should be routed to OSL. Usually, yes, they do physically re-tag, so someone can quickly know where it goes next without a scan. In fact, at some point when it gets changed, next scan should prompt a physical re-tag.

Never a bad idea, especially in IRROPS, to check with the next flight operator to make sure they received it - If they haven't, they can work to request it at transfer point, vs. at destination. Depending on timing, it still may not make your flight, but depending on frequency, can help it get on the next flight vs. having to wait until after you land to start this process.