Ah, my bad, I misread what you're saying - you need to grab the core to advance the mission to the next step, but you don't need to actually hand it in, so e.g. if you sell it by accident, it's fine.
Edit: and, yeah, I suppose it's possible to break the tutorial this way! But, well. I think there are probably other ways to do that as well; it's not very on-the-rails in general.