Final answer:
The parent's statement that indicates further teaching is needed is when they suggest stopping the antibiotic ointment when the eye drainage improves.
Step-by-step explanation:
The statement by the parent that indicates further teaching is needed is c. "When the eye drainage improves, we'll stop giving the antibiotic ointment."
In bacterial conjunctivitis, it is important to complete the full course of antibiotic treatment prescribed by the doctor. Stopping the antibiotic ointment when the eye drainage improves can lead to incomplete eradication of the bacteria and the possibility of the infection recurring.
To ensure the proper management of conjunctivitis, the parent should be informed that it is necessary to continue using the antibiotic ointment as prescribed by the doctor until the treatment is completed.