When we were young
Anna was a victim of such types of schemes herself and she knew what it felt to be in the Madam's position. Her case was better because she met Mo Xing who eased all of the pain away but not many people were lucky to find for themselves people who would help them go through whatever it was they were feeling.
The madam was a good example. She was carrying around the burn scars afraid that if she did away with them then the reason for her revenge would also disappear.
She wanted them to be a reminder so that she could use everything she had to seek the justice she so deserved and then her heart would finally get peace.
Anna was looking for justice for her and now she wanted The Madam to have a new start by removing all of her scars.