I agree that you will probably have to cut out a whole piece and 'insert' a new piece. What about making a statement with the pieces? Such as piece this with a heart shaped and mark it like a label - made by grandmother. Or make a square but applique something on the top block. Is there a special memory of the grandmother? maybe teacup or flowers? I would take whatever fabric I was planning on using and wash it several times to soften it - or maybe fabric salvaged from an old dress or shirt.