There are times when there is a report sitting on the homepage but when hovering over the right hand corner of that report, the pencil icon does not appear. This makes it difficult if you wish to modify this for that user.
This is because this report was not created through the normal report application but rather it is a predefined filter placed on that homepage.
Follow the steps below to find the filter.
You should then be presented with the filters that have that name. You can further drill down by finding which user it is assigned to as well.