The last bank I worked at was much smaller than the one that I work for now.
At the last bank all errors on CTRs required a new form to be completed by the teller. This was a good way to keep the tellers really paying attention to what they were doing when submitting a CTR to us. However, it did have the potential to hold us up if they were not prompt on getting the new form sent in. As a result, there were times when we combined the two options you present. We made the necessary corrections if we could in back room but still made the teller do the form over again.
One of my personal favorite tactics.
At my current institution it's simply not really a good time management option to require 'redos'. The way the bank is structured does not lend itself well to the practice. All corrections are made backroom and any specific teller or branch that generates a higher error rate is given refresher training on proper completion.
Note, this is only applicable to errors that we *can* correct. If the problem is missing information, that's obviously something that is sent back to the front line to get cleared up A.S.A.P.