I donate t-shirt scraps for animal beds! Place the scraps in a 'pillowcase' type bag BUT stitch sections off so that the t-shirt fabric is separated. That way all of the heavy fabric won't go together into one 'glob' in the washer and dryer.
Make your case, stitch down the center perpendicular to the opening, add some scraps, stitch horizontally to opening, add some scraps, stitch horizontally, etc. EASY!
Don't make them too heavy that it takes too long to dry.
Nan