I really can't see the "damage" in your pic, but do find in my own use that vinyl (PU film) has a tendency to hold creases when folded, so, especially with larger areas I often either fold differently, or just stack for clients.
As for laundering, I notice on the tech and care sheet for Sisar Easyweed, they specifically mention that the stuff is "Iron Friendly". So, even though, over the years, I was always a little surprised when folks talked about ironing their T shirts, it appears that the problem that you are encountering seems to justify it.
Though the trend over the last ten or so years has changed towards "fashion" weights, the stuff is just not as supple as most inks.