Sometimes the dullness that is left behind is the actual residue of the poo itself. You can try to dissolve this which “could” lighten the stain. In most cases you are still left with the actual etching itself. Again, trying to dissolve the residue on the surrounds of the etching helps mask the damage, which makes it much harder to spot. If the etching is pretty serious, then compounding the area with a decent swirl remover is your only other option. So far I’ve been lucky with dissolving the stains and not having to compound.
Steps to dissolve the stain with an acid wash:
Mix a 50/50 solution of white vinegar and distilled water.
Place a paper towel over the affected area and spray the above solution (using a spray bottle) so that it saturates the area
Allow this to sit for about 15-20 mins.
Wash off with a normal shampoo
Repeat if necessary.
If found that this radically improved by bird poop stain, and I didn't even have to compound !
Good luck…