Robert and Dorcas Saxtorph wait to be boarded by kzinti. As they embrace, he thinks about the robot prospector which they have sent onto the surface of the tnuctipun artifact that encloses a decaying and radiating mini-black hole. Then:
"Saxtorph lurched where he stood. 'Fanden i helvede!' he roared." (Man-Kzin Wars III, p. 286)
What can this be but yet another sudden moment of realization? The kzinti are a mortal problem and thinking of the robot has made Saxtorph realize the appropriately destructive solution. I have read the story before but did not remember what the solution was. However, it is simple and straightforward: make the robot crash onto the artifact, thus opening another gap in its surface through which lethal radiation can pour out in the direction of the kzinti ship. The Saxtorphs disposed of kzinti by simple maneuvers in the system of the red dwarf star and the same approach will suffice here.
This kzinti crew is indeed killed but the story does not end there. Several loose ends must be tied up first.