Can I use a Wok ring on a gas range?
I find it amusing that your range warns you the cooking ring will work as intended.  It's supposed to be heat trap, and focus heat on the bottom of the wok.

That said, they are also correct that it may discolor the burner grate.  I can't really say what your grates are made from, and many cooking materials discolor at high temperatures.  I think the main idea behind this paragraph in your manual is to save them from warranty replacements for discolored grates.

I also find it highly suspect that a wok could damage the burner itself.  They are usually ceramic, in direct contact with open flame, and any pan traps heat to some degree.  Burners get HOT and have to be able to take it.  Although the little decorative cap on the burner might discolor as well.