A fun little story, I have no real complaints. It reminded me a lot of Dunesteef's Anakoinosis, with a culture clash with fuzzy little aliens demanding we dominate them for their own happiness (in that case slavery, in this case murder).
I couldn't help thinking about the repercussions of the social system that these little alien buddies have worked up for themselves. It would make dishonor very hard to expunge since suicide is forbidden and murder only transfers it. One would have to die of natural causes to properly expunge it, so it would be very easy for the whole society to build up a poisonous dishonor that it has a great difficulty purging.
And I got to thinking about how one could purge the evil. The idea in the story was a good one for getting rid of this, getting an outside race. For me, this kind of reminded me of a national policy to get rid of toxic waste. Country A is rich and has an environmental agency which forbids the dumping of toxic waste within its borders. Country B is poor and has no such regulations. So Country A pays Country B for the right to dump the waste in Country B. Country A meets its self-imposed regulations by not dumping in its own borders, Country B makes money that it didn't have before to feed people. The same came to mind here, but with countries being species, and toxic waste being dishonor.
Another way that I thought of is to use terminal members of the species as a dump. You find someone who is dishonored and likely to die soon (through old age or terminal illness), and you have them maim as many dishonored members as you can, lining them up one after the other. Then when they die they expunge all the dishonor with them. I guess whether this would work depends on whether that individual would agree--is a lot of dishonor very different from a little dishonor, especially if you know you're going to die? I guess I'm not really sure. So maybe this isn't a great plan because you wouldn't get a willing participant...