Can I place my gas range top grates in my self cleaning oven to clean?

no......soak them in the bathtub with blue dawn dish soap to remove the grease

yes you can

I put mine in the dishwasher.

Many manufacturers recommend taking the racks out when self cleaning, part of the reason for that is the heat destroys the coating on them.

You are talking about the racks inside the oven and she is talking about the grates on the top of the stove that pots and pans sit on. I wouldn't do it. Put them through the dishwasher.

I just read on DIY about soaking them in the bathtub and I think it was vinegar water. Just check the website for answers.

top grates not racks

I would soak them first, scrub them and then run them through the dishwasher.