Not taking a restraining order as an answer, the Alaska Elections Divison appealed to the state Supreme Court for a stay of the order and got it, with some restrictions.
The Supreme Court's order (PDF) does say that the list cannot include the candidate's party affiliation or any other information, however, and also calls for the segregation of all ballots cast by voters provided with the list of write-in candidates.
The Court obviously expects continued litigation in the issue, and the very real possibility that this election goes into recount territory and these write-in ballots will be the core controversy. The Democratic Party, likely with the support of the GOP, will file to ask the court to take up their suit.