I knew water should not be going between the gutters and the fascia boards. I think that the gang that did the roof and the gang that did the gutters didn't talk to each other.
My first fix was to pull the lowest piece of roofing material out from behind the gutter. There were two areas that this didn't seem to fix. Home Depot has some L-shaped "roofing" pieces that did the job nicely. I don't think they're a long-term solution but we've been having some wicked rain.
I'm torn between telling the people that did the roof to come back out and fix what they did and getting someone out that knows what they're doing.