Repair Marks on doll's torso

It looks like sealant residue to me, especially if you gently run your nail on it and feel some degree of texture. I hope it won’t be too hard to remove! It has to be quite old!

 

It does look like sealant. I would try washing it off with a suitable solvent (anything safe for removing face ups should work).

I would only use the eraser as a very last resort for something like this. Keep in mind that it's and abrasive. If you are not super careful to only rub at the sealent itself you may end up buffing the undamaged surface around it as well while the surface under the sealent is protected. Especcially in an older doll this could give a blotchy colour difference to the area.