I think you need to do the following in your local desktop database:
- remove child profiles from box set (in the parent profile, box set content section)
- Probably delete the child profiles
- sync again with you i-device

Just guessing, haven't tried it yet

I'll add: I'm doing this because I like to see both my parent and child profiles together on my thumbnails without having to open up the boxset. And yeah, removing the children will still show the parent with an icon which can be opened - to show empty contents, which seems wrong. Thank you for submitting a support ticket.

Steps needed to remove Box Set icon from iOS Profiles:

1) Remove the entire Box Set from collection in desktop DVDP
2) Update DVDP iOS
3) Re-add the title to your collection in desktop DVDP. When asked if you want to Add these Child Profiles click NO.
4) Update DVDP iOS (Profile in DVDP iOS now has no Box Set icon).
5) Flag the title in desktop DVDP and select Collection>Flagged>Check for Child Profiles and add the Child Profile(s) to the title.
6) DO NOT UPDATE YOUR DVDP iOS AT THIS TIME
7) In desktop DVDP edit the Box Set and in Box Set Contents remove the Child Profile(s).
8) Update your DVDP iOS
9) SUCCESS!!!

Your title in DVDP iOS still has no Box Set icon and the Child Profile(s) is/are also in your collection.