Our shelter uses towels, blankets, etc that can be easily tossed in the wash, disinfected and dried. Pretty hard on piecework.
Making a quilt for a fundraiser might be a use for your cuttings. One of our local humane societies has a thrift store. Perhaps some quilter would like to purchase zip bags of scraps.
Bless you for your concern. God sees even the fall of the sparrow.