Sorry, Firefox Home for iPhone is only able to display bookmarks synced from your PC; it cannot edit them. If you edit or rearrange bookmarks on your PC, the changes will sync to your iPhone.

Oh, that's a pity! I would have thought they'd at least have that basic level of service for it.

As my desktop is cluttered full of the rest of the family's bookmarks too, is there any other way to rearrange the desktop for my phone without losing what's on it?

Using desktop Firefox, you could put all of your personal bookmarks into one folder. Then on either your phone or your desktop, you could just click on that folder to view your own bookmarks.

A more complex solution would be to create your own Firefox "profile" on your computer. For details, see: Profile Manager - Create, remove or switch Firefox profiles

Thanks for that.