Firstly, let's give a definition of what protected means within the StackExchange context:
Protected questions have the additional restriction that new users are not permitted to answer the question. Unlike locked questions, they can still be edited, commented on, and voted on. You can even vote to close them.
Furthermore on the motivation of protecting a question:
Some questions are protected because they are expected to attract either spam or users -- often new users -- who may mistake the site as a traditional forum, posting "noisy" answers such as "Thank you" or "This worked for me" or "I'm also having this problem".
Taken from: What is a “protected” question?
Next I looked up the definition of protected on dictionary.com:
to defend or guard from attack, invasion, loss, annoyance, insult, etc.; cover or shield from injury or danger.
This definition seems pretty spot-on, especially when you shorten the definition to: guard from annoyance
Now looking at the definition of restricted:
limited to or admitting only members of a particular group or class
Now this seems accurate, except when you consider new users can still look at the question and interact through: comments, votes and edits. You would need to be more specific and say something like Answer Restricted.
Just to explore some other options I had a look on thesaurus.com, and the key synonyms that were appearing included:
Shielded, covered, guaranteed, preserved, secured, sheltered.
In my opinion:
covered can be dismissed it gives the impression of concealment, but new users can still look at the question.
guaranteed can be dismissed because spam is not guaranteed to be prevented.
preserved can be dismissed because it is more to do with maintenance and retention.
secured can be dismissed because it is too absolute.
sheltered can be dismissed because it creates the imagery of established SO users hiding inside whilst new users claw at the doors trying to get out of the rain.
Again shielded creates similar imagery of keeping new users at bay. Essentially this is true, but the objective is to reduce spam and not directly oppose new users.
In a nutshell, after exploring some synonyms and alternatives, I think protected is the best word for the job.