The ring

So, the wife loses the ring in the past, and her husband sees her losing it in a vision. So he goes to the spot and finds the ring. (Which makes one wonder how much geography changes in 10,000 years.)

The husband gives the ring to the pilot, who takes it into the past and then gives it to the wife. So now there's two identical rings in the past. What if they went and found the ring she'd lost?

Also, you would think that the husband would've used this mechanism to allow the pilot to communicate with him. He could leave something near the same spot (like an engraving on the rock) to let him know he'd successfully made it to the past. That way, they could send down unmanned drones to provide food and supplies.