Does the use of materials and things on the teeth during orthodontic maintenance invalidate the fast?

Using toothpaste or a miswak does not invalidate the fast, as long as the fasting person does not intentionally swallow anything from it. It is preferable to do this at night as a precautionary measure.

Sheikh Ibn Baz was asked about the effect of cleaning, filling, extracting teeth, or taking an anesthetic injection on fasting. He replied that this does not affect the validity of the fast and is excused, provided one is careful not to swallow medicine or blood. The aforementioned injection does not affect the validity of the fast because it is not in the meaning of eating and drinking.