The box and text can't be edited, but the rules governing it are under Publishing->Set Publishing Options->Animal Selection.
thanks is there a field that I can pull and put on a report "Available for Adoption" / "Not Available for Adoption"?
Not for a report, the status is calculated on the fly and not stored anywhere. I think we do have a task on our development list to do something about that. The existing reports test the IsNotAvailableForAdoption field, which is whether or not the flag has been manually set to say the animal is not adoptable. You can view animals by their status in Shelter View (pick Status from the dropdown at the top right). You can also add the virtual field "Adoptable" to your find animal results screen under Settings->Options->Find Animal/Person. This column shows the reason the animal is not adoptable.