Help with ironing a skirt please

My mom just bought herself an ultrasuede skirt that is now really wrinkly. She took it to a dry cleaning place, but they want $27 upfront and require that she sign a release form for it in case the skirt is ruined. If there’s nothing else she can do about the skirt, she’ll have to take it to the dry cleaner’s. However, I was hoping there was something that could be done to get rid of the wrinkles without spending all that money and risk ruining the skirt.

Any help would be greatly appreciated. Thank you!

They say, for leather (not suede):

But I would guess that you can do the same thing for suede but I would probably iron it inside out so you don’t flatten the nap and maybe with a towel protecting the garment itself.

And this place confirms the towel idea:

As does this place:

Here’s the Ultraseude care instructions:

Thank you so much, Sue Duhnym and Squink!