I agree with other answers that puncturing the balloon and letting the payload fall to a lower altitude for capture would be the way to go. I don't think it would be reliable though because the balloon does not have a designed grab point like various re-entering space capsules have had.

That said, the Lockheed U-2 is still in service and has a service ceiling of 80,000 feet or more. There are some high-altitude drones that get into the 70,000 feet range, such as the Airbus Zephyy. Although I don't know what such an aircraft could actually do about a balloon. Trailing a grappling hook seems a bit too Looney Tunes to work.