I haven't seen one of these dampers, so I don't know how deep the engraving is. If you paint over the engravings now, with white paint, and then remove the paint from the high surface, you will be left with the engravings marked again.
If there is just too much paint on the damper, you may need to start again and put less paint on, and then try the white paint trick.
If there is just too much paint on the damper, you may need to start again and put less paint on, and then try the white paint trick.