Should the Party Kill Arrigal?

Arrigal is an assassin, or at least, that's what his Statblock says. As far as the story has canonically established, he has never killed anyone. His assassinishness is not why the party wants him dead. The party of adventurers in the D&D game I run every week want to kill Arrigal because he stole from them, but (aside from the fact that killing is not a suitable punishment for theft) the main moral complication to their choice of action is that they stole from him first.

Arrigal is the most competent member of a group of travelers called the Vistani. A few sessions ago, one of the members of the adventuring party broke into the Vistani Treasure Wagon and stole almost all their valuables. Once he had deduced who the culprit was, Arrigal set out to steal it all back. He succeeded, though he had to knock out two of the adventuring party members out to do so. Yet, in his haste to perform his burglary work quickly, he stole more from the party than they had stolen from the Vistani, and they now want to take it all back, along with his life.

Granted, I think that the party is partly justified. Some of the goods that had been stolen from them had been earned legitimately, and they deserve to have those goods returned to them. Yet, if they would argue that Arrigal deserves to die for the crime of stealing from them, it could also be argued that at least one member of their adventuring party deserves to die for stealing from the Vistani. Justice is blind. If stealing is a capital offense, then stealing is a capital offense.

Personally, I don't believe that Arrigal deserves to die for what he did. Yes, he stole, and he hurt one innocent person to do so, but he did so only to steal back that which had been stolen from him and his group, and he made certain that no permanent harm was done. The party wants the rest of their stuff back, and I mostly sympathize with them, but I do not sympathize as strongly with their desire to kill Arrigal, and I don't think that they'd be morally justified in doing so.