How do I season the griddle that came with my new gas stove?

It is a Gas Stove. It can only be worked on by a registered gas technician who will supply and fit the parts. It looks like 'Revelation' is the model number.

https://www.google.com/search?q=Tappan+Revelation+Gas+Stove

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season the thing

Could be you have been cleaning your griddle too vigorously and perhaps you should re-season it - google search seasoning a new pan...

They must be converted. New burner orifaces for burners, griddle, and oven and a new regulator for the gas valve.

my griddle is also heated with propane and makes this noise. i have come across another home with propane and a wolf griddle that also makes this noise...did you resolve this issue, cause I'm interested in the result you found?

Could be the thermostat.
Range repair in Mission Viejo, CA
Appliance repair in Mission Viejo and Orange County, CA

I just got a new range and the instructions to season the griddle are in the instruction book. Wash an d dry the griddle. coat all surfaces ( top and bottom ) with a thin coat of cookin oil. place in oven at 350F for one hour. turn off afer an hour and let cool in the oven.

wipe it down with olive oil and heat it up then let is cool completly and wipe again do this 4 or 5 times and you will be good to go

I have a Thermador Gas Range PG364GDBS - Oven, 4 burners, and center griddle. All are gas. The four burners and gas oven work fine. The griddle just stopped working, no spark. Turning on the griddle control, the gas valve opens(hear it), gas flows (smell it), but the ignitor will not spark (no loud or faint spark that I can hear). I got a replacement ignition device (mount at the burner) thinking it might be the problem, but still no spark. I checked the AC voltage at the terminal and measured 39 VAC between the terminal and ground. Not sure if that is the correct voltage. Any insights or advice would be great.

This addresses the cleaning question only. I was a chef for 27 yrs.  Once the griddle surface has begun to rust, and this can and even will be the case on a new stove, you have to get agressive with it. You're going to use sanding tools and oil. 
If the griddle top is heavily rusted, I use my electric palm sander fitted with fine emory paper (the black stuff that can get wet). Wet down the surface with a small amount of oil and work the sander evenly over the entire surface in rhythmic strokes from front to back or side to side. I don't have a scientific reason for this but my gut tells me not to work in circles or random strokes. Try to work the entire surface evenly to avoid creating high or low spots. Use a straight edged spatula or I use a dough cutter (flat edge of about 4" and available from culinary store for under $10) to cleanly scrape  the dirty oil off the surface. Sand in shorter durations & clean often to avoid grinding dirty flavor into the surface. 
Once you have it clean its time to season it. With a better oil focusing on flavor, spread a thin layer over the surface and cook at about 250 degrees for 15 - 20 minutes. Repeat this after every use until you build up a layer of cooked oil almost like enamel to resist rust between uses. This makes a teflon like finish to your griddle.
For regular use and cleaning scrape down immediately after cooking and while the griddle is still hot. When its cool use a hand sanding block you can get from the hardware store. The one I prefer is a firm sponge with emory paper wrapped around it. I store this in a bowl on the shelf above the stove because it is oily and dirty. Alternately you can also use rock salt and a kitchen rag to loosen food particles stuck to the griddle but this makes for messy laundry or throw away rags. We also use viengar or lemon juice and water to loosen food while the griddle is still hot or warm. NEVER USE SOAP!!!!!! You want your food to taste good don't you?
The oil used for cleaning can be anything with minimal flavor like canola oil but the oil used for seasoning the griddle should be a high heat type like sunflower.
Personally I only cook in black cast iron pans and the above method is how I treat them as well. Rock salt and water is all I ever need to clean them between uses.
Rick Casey