Cleaning indoor grill?

I have a Breville indoor grill, similar to the George Forman grills. This unit does not come apart for cleaning, so I was wondering if anyone had any ideas on how to clean without causing a mess and taking 30 minutes. Thanks!
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I have a George Foreman, which does not have the removable parts. Cleaning it is actually VERY simple and only takes a minute. When I finish cooking something, I unplug the grill. I wet a couple of paper towels, wring them out and flatten them out and put them on the grill and close it. I go eat my meal. When I'm done eating, I open the grill and take the paper towels out and wipe the grills with a clean wet paper towel. Thats it.
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