Translation:You don't need to take notes today.
Your suggestion seems to have a typo in it. 取らなくてもいいです might work but it sounds a bit more like anime to me. Let's let an expert tell us.
I'm no expert, but 取らなくて(も)いいです actually sounds more natural than 取らないでいいです...
Which words equate to "need" here? This seems to be a loose translation. Not saying translation is wrong, I just dont understand how "need" is inferred.
Nothing in this sentence literally equates to "need". The closest natural translation is probably something like "today, it's okay to not take notes".
Personally, I wouldn't go so far as to say that equating "it's okay not to" with "there's no need to" is a "loose translation", but I can see what you mean. It takes a step away from a literal translation (which isn't necessarily a bad thing) for the sake of understandability in the target language (which is usually a good thing).
撮る is exclusively for taking (as in capturing/filming) photos or videos, while 取る is for physically taking just about anything.
Alternative: You need not take notes today or You have no need of taking notes today.