ArtMetal

You are working with galvanized wire cloth.

That is steel that has been fluxed and dipped in molten zinc.

Zinc melts and 780 and burns with a bright white flame, releasing poisonous oxide smoke. Breathing that can give you metal fume fever. Chills, aches, nausea, and worse if you get a bad dose.
The good news is that zinc is used by the body as a nutrient and will be cleared from your system. That does not mean that an overdose won't kill you, only that if you live, you will probably get better.

Get some stainless mesh or even uncoated steel.
the stainless will get a black oxide on it from the heat and shouldn't stick to what you are soldering.

(note, once the zinc has been burnt off, those grates may work, just don't burn it off inside or stand upwind of it)

Gene Olson
Sculptor
Elk River, MN