Umbilicial cord

My little one is nearly 1 month old, their umbilical cord fell off around day 10 and they still have what looks to be a bit of the cord in their belly button. I spoke to health visitor about this and they said it would clear up with her being bathed and dabbing it with Luke warm water. It’s been over a week since then and no difference. I can’t find anything online about this and I’m starting to worry. Does anyone have any advice? Is this normal?