If you gave it back, you can't claim it again, but not sure what happens if you delete without returning the challenge first.
This is one of those gosh-darn bugs I've been going on about for a few years.
Short answer: no.
Once you delete the template and it has that quiz title, the system automatically believes that you don't want to write that challenge quiz, and if you try to reclaim it from the challenge list, it will lose its challenge designation when the site has its maintenance period early in the morning, so it will still be a quiz...just not a challenge quiz.
Long answer: yes?
The way to circumvent that loss of designation is by renaming the quiz. If you add even one letter, the system will be tricked into believing your deleted quiz is still deleted and there's nothing to worry about. If you slightly change the challenge title to 'Believe It or Do Not' or 'Believe Me or Don't' when you create it the second time, the system will believe you're doing A-OK.