Supposedly, the Zone system originally allowed a limited number of law enforcement personnel to deal with planetwide unrest and crime. The crime has gone away now - but as far as we can tell, no element of the system has been discontinued or diluted. The law enforcers still exist to pounce on any crime taking place in a Zone, and the punishment still is death. One miscreant getting away by using alien technology should not change any of that - the Edo would still live in mortal fear of taking a misstep.
The true implications would be religious: the Edo God was actively involved in allowing the aliens to escape. Or at least God first demonstrated its ability to prevent an escape, then chose not to use that ability. Would this be taken to mean that God, a mysterious entity that supposedly doesn't express its will clearly in its rare dealings with the Edo, takes a dim view on the Zone system? If so, the Edo would no doubt start at least experimenting with dismantling the system, and waiting to see how God reacts.
Or would this be taken to mean that the Law still applies for the Edo, but alien visitors from now on should be treated as immune to the Law? This could be implemented easily enough, considering how rare alien visitors apparently re. But would this cause discontent on an abstract level, with the Edo feeling they are inferior to space aliens?