As far as the cursed items go, I think you could teleport away without it but it would instantly appear back with you. Like a cursed ring would appear on your finger or a non worn item would still appear in your equipment, etc. As far as the Iron Bands are concerned, I haven't read them, but I don't think they're cursed items and could be left behind.
I only brought up the dim hop because it was part of our convo at game.