PLEASE do not give fabric scraps or yarn to birds. For one thing, the threads can get wrapped around the bird's leg(s), cutting off the circulation. The leg(s) will eventually die and fall off. Secondly, if the fabric scraps are used in a nest, they stay too wet, causing mold and mildew. Baby birds are very fragile, and this can make them ill.
Source: Personal experience! I used to raise finches, and yes, they do enjoy fabric scraps ... until the day a loose thread got tangled around one of their legs. Luckily I noticed it before any damage was done. No more scraps! Another time, I bought some nesting materials from a manufacturer, and didn't notice it had tiny hair-like threads in it. One would think that it would've been checked for safety before it was advertised for sale! By the time I noticed that one of the threads was tangled around one of my bird's legs, it was too late. The leg was too far gone to save it.