I am attempting to write a Player Author Challenges quiz. I accidentally deleted my first attempt. I am trying to rewrite the quiz. I am getting "quiz deleted" as I am trying to reclaim this title. Can I reclaim this quiz title?

In a sense, yes. The system will always allow you to reclaim a title from the list. The problem is that once you delete the quiz once (or abandon the challenge once) the system always believes that you do not want to complete that challenge, so when the site does its daily maintenance, it will make its checks and remove the challenge designation from your quiz. The only way around it would be to rename the challenge quiz, which kind of goes against the rules, so that the system believes you're writing something else.

I reclaimed the challenge title and got my quiz online. Yet I didn't get credit. Oh well. On to the next quiz.

The title needs to be changed at the template creation stage; if it's done at any later time, the site will believe it to be the old quiz and effectively remove the challenge designation.

So can this be done if the quiz is already online?

Or did I just ask a silly question?

Never a silly question.

You would need to reclaim the challenge and make a new template; an existing template can't be given that designation for the same reasons we can't switch a regular quiz template to a photo quiz template or a match quiz template. It all comes from the inception of the template.
There's no way for an editor to control this from their end, unfortunately, because it's just not built into the site code.

I guess it would difficult to get credit for it now. I'm going to move on. I would suggest the title be taken off of the list to prevent repetition.

Done.

Thanks!