You must have the sort order for the list (regular or smart) be set to Drag and drop.

In order to change this, click on the list name in iOS and choose Change xxx. Select Drag and drop, go back and choose Change (top right).

You get the small ribbons on the right, used to move the tasks.

Ah so when you are in the desired list if you click on it and choose edit list I see it now.

Hey thank you so much for your help. Probably seems silly but this is a big deal to me :-)

Had to search around a bit before I figured it out, it makes sense that the setting has to be right.

It would be nice to combine drag and drop sort order with grouping. For example in the This Week view, to be able to drag to reorder tasks within a day, or even move them between days.