Is there any reason not to tell Eric ourselves? We can pretty easily hide Justine knowing us by saying that it was the call from Barton that put us on the trail. It lets us tell Eric that we discovered the problem, and track down the ring, so that we can warn him that if he doesn't decide to bring it back, he might be in lethal danger. If he is really as obsessed with wakanda as he sounds like, he might jump at the chance to return something to a representative and maybe get a reward for doing so. The only problem is our telling Barton that we already knew about the issue, but if we just text him that our cover story was that he was the first we heard about it for secret identity reasons, I'm pretty sure he won't tell Eric.
It seems unfair to everyone involved to not make certain that Eric knows the danger inherent to keeping the ring, and honestly it's his at the moment so he should be the one to make the choice. Ideally with Justine there, since that lets her know whether her guest is currently keeping something that might get them both killed, and let them talk to each other about it.
edit: something like this maybe?
[ ] Tell Eric yourself. Explain what you can of the situation without revealing your or Justine's identities, and tell him that someone from Wakanda is tracking it. You're pretty sure that part is handled for now, but he could still be in danger. It might be best for everyone to give it back voluntarily, or at least take precautions.