We have the rangetop with griddle also. Here's what you do:

Go to a restaurant supply store. Get the 3M griddle cleaning pad/system. It's called the #461 Griddle Pan Holder, for use with Scotch-Brite #46 griddle polishing pad and 3M #200 griddle screen.

It comes with the polishing pad and griddle screen.

After using the griddle, let it cool down until it reaches 180 degrees (approx). Put about 1/8 to 1/4 cup plain water on the griddle. Using the holder and the polishing pad (not the screen), scrub the surface following the grain. It will loosen all the stuck bits and melt the grease. The pad will soak up a lot of the gunk.

Follow with a plain paper towel wadded up to sop up as much of the water and grease as possible.

Repeat with more water and the pad if you need to. You will be able to get most of the stuff off. You don't want to polish it to a shiny new metal finish, or you'll have removed the natural seasoning.

Pour about a teaspoon or so of plain vegetable oil in the center, and using a paper towel spread it on the griddle. Let cool and put the cover on it.

Sometimes I just let it cool completely after cooking, then clean it the next day or when convenient. I heat it up until it gets to about 180, then follow with the screen.

Never use any soap product on the grill. It will get a patina after time...a slight tan or yellowing, which is normal. Once or twice a year, you can use the screen to deep clean the griddle, but it tears the seasoning off completely and you have to start over, seasoning the grill with oil as the Wolf instructions say to do.

If it's really dirty, you can use the enzymatic cleaner for coffee machines (called Java Kleen). You put a little on the grill then scrub with the pad. It's non-toxic...be careful of "grill cleaning" products in general...they tend to be quite toxic.

Any good restaurant supply store can provide these things and tell you how to clean your griddle like the professionals.

Wonderful advice!! Thanks so much!