As a TA, I used a Scantron machine a handful of times. A small tear on the side likely won't affect how your answer sheet is graded.
If you're absolutely paranoid, just have them manually grade it, as @"Cant Get Right" suggested.
Hey, thanks so much for all of the responses! It's helpful to know how you all approach it. I definitely will wait until after BR to grade my tests. I am slotted for June, hopefully I am around the mark by then, so I don't have to push it back.