Our house is ten years old and has integral gutters (aka Yankee Gutters) to drain water off of a concrete tile roof. Given that we live in Vancouver, we get a fair amount of rain and the gutters get a pretty good work out.

The integral gutters are made of a tar covered membrane and are not solid metal channel like I have heard about elsewhere.

The issue I am having is with one short section of gutter that doesn't slope properly. In short, water doesn't move to the drain and pools there and sits. I am worried that the water sitting there will either damn up in ice conditions or eventually seep through the tar. If this were a normal gutter I would remove and fix the slope. But given it is an integral gutter, I don't know how to do this.

Do you have any suggestions?