My 2 cents: Your Grandmother's quilt came in the mail in an inadequate package and could have been further damaged.
What does this tell you? If the quilt was loved and precious to you, wouldn't you treat it with care when you sent it to be repaired?
Before you move forward and repair this quilt putting in many hours, and most importantly your heart and memories of your grandmother......ask yourself this.. Will the quilt be treated with care ....after you send it back to your aunt? Only you can answer the questions and decide what you feel is best.