the internet will heal you
No, really. Do some searching and see if you can figure out how to dismantle the door, and put it back together. Start by typing the name and model number into your search engine, and go from there.
I just went and looked at mine. It appears to be held together with little Torx fasteners. If you want to take yours apart, and a gasket is available for that piece, get the gasket before you proceed. Otherwise, water + wiring = a dead dishwasher if you are lucky, or a dead or injured person if you are not lucky. And the doors cost almost as much to replace as the whole unit.
Another option is to call the repair shop and find out how much it will cost for them to do this. I know some appliance repair people, they are used to seeing every kind of pest and won't be surprised. Cockroaches in the dishwasher beats rats in the stove any day.