Ask them to provide documentation about what damage actually exists and what they are doing to repair it. Damage: are they talking scratches, gouges, cracks? Repair: are they applying new enamel, overlaying a new acrylic liner, or doing a full replacement of the tub? Is it being restored to like condition, or are they making other changes like color or style? If they are making changes, you should only be responsible for the portion of the money that brings it back to the condition it was in when you moved in.
Did you take pictures of the bathtub before you moved out? You may be able to argue it’s not in that bad a condition.
Did you take pictures of the bathtub right after moving in (or was it noted on a condition report when you moved in?) If so and the pictures are similar to what you took right before moving out, you may be able to argue the tub was in that condition when you moved in or you only contributed reasonable wear and tear for which you can’t be charged.
How old is the tub and what was it made of (I.e. acrylic, cast iron, etc.) You may be able to argue that the tub is at the end of its natural life expectancy.
Tip: take pictures of the move in and move out conditions of wherever you live. Even if you’re the owner. Even if it’s boring stuff like empty rooms and blank walls. But especially any blemishes like poorly repaired holes. They can come in handy in the when stuff like this comes up.