Is this a muslin background? If so, they should never be folded. I always stuff mine in a duffel bag. Wad it up good and tight and let it sit for a few days. Then use a large f-stop in order to get shallow depth of field and a pleasing background blur.
I have tried this both ways.
The first way is - ironing. Hot and sweaty work, and you will forever be worried about any little potential wrinkle...
The best way is to keep it "perfectly wrinkled":
Moisten slighly - with a (whatever it's called - little spray bottle thingy which makes a mist). Then crumple up. Crumlple again. And again. Putting it in a wad on the floor and jumping on it can be fun, as can be kicking it around for half an hour or so.
Leave to dry.