I've found a way to use my leftover batting scraps. Or should I say, "another use." I like to use them for little thread catchers beside my sewing machine. The ones pictured here measure about 1 1/2" by about 3 1/2." "About" is the operative word, as they are definitely cut free-hand. They could even be bigger than this.
After they get filled up with lots of thread scraps, I just lift off the top piece, fold it in half and throw it in my bin of dog bed filling. The thread seems to really stick to them!
At another sewing machine I have some cut into circles, as they fit that space better.