A statement by the mother that indicates that she understands the instructions would be: "I will watch for redness, swelling, warmth, or drainage at the site of the old IV. If any of these signs of infection appear, I will call the doctor right away." This shows that the mother understands the importance of monitoring the site for potential signs of infection and taking action if necessary. It is important for the mother to be aware of these signs and to take prompt action if any of them occur, as neutropenia can increase the risk of infection and it is important to address any potential infections as soon as possible to prevent further complications.