When I've been in charge of record review in the past, when I found improper "corrections" (scribbles, write overs, etc.), I made it a habit to go find the employee responsible, have them write a small number next to the bad mark, then copy that number down at the bottom or back of the page and write an explanation of what the mistake had been with the date. This makes the case that, even though the originally writing can't be written, you at least have the employee's statement on what they wrote incorrectly directly on that form. It also shows that the person reviewing the forms for accuracy is doing their job.
Always a chance an auditor will find an issue with that. If they go through your batch records and find the same employee screwing up documents constantly, they'll expect to see retraining as a corrective action. But hell, it's better than what my production manager used to do: have the employee sit at a desk and recopy the entire record cleanly onto a new form.