Is this a finished quilt? Or just a top?
I think the answer depends on the condition of the quilt.
One cold-hearted way to look at it - if this quilt was made by a stranger - what would you do with it?
Another way to look at things- if grandma baked a batch of wonderful cookies - and you ate all of them - would you feel quilty that you did have one left over to remember her by?
Perhaps take several photos of it - front and back - and you could keep them as a remembrance of the quilt?