Tapping the red button in the lower right will put either list into “Edit” mode. This mode is available for both the Event and Guest lists and allows you to .
What may not be obvious is that you can change the order of the list by touching the icon on the right edge that looks like three horizontal lines; this is an order control icon and it does just what you might expect; you can drag it up and down. Just touch it and hold for just a moment and list row you touch will lift slightly; as you drag your finger up or down in the list, the entry will follow you and others will shift around to make room. And finally, it will stay wherever it is when you lift your finger!
Sometimes the interface is very forgiving and other times, it requires a certain amount of precision; in this case there are icons close to each other that trigger different behaviors. Care should be taken to only touch the icon you want as others can cause unexpected behavior; for example, the adjacent icon will take you to the Edit screen and the Title or the Badge will simply navigate to the Guest list and take you out of Edit mode.