This kind of scratch is actually irreparable and under normal circumstances you can only replace the case or put a phone case directly. Scratches can also be repaired with toothpaste. First of all, wipe the scratched mobile phone clean, take a clean and soft towel or paper towel, and twist off excess water after wetting.
Squeeze half a centimeter of toothpaste onto a wet paper towel and gently and evenly apply the toothpaste to the back of the phone case.
But you can still see the micro-traces of scratches, if you replace the phone case or buy the phone sheath is much better