There are 2 check boxes on list page one is for deleting permanently from Redback labeled as Delete From RB and other is for deleting from list labeled as Delete From List. Please check products you want removeed from the list under label Delete From List and then press Delete button at the bottom, this will remove products from list only. Below is a screenshot for reference.
There are video guides underneath that will guide you through the entire process
Video Guide to Acquire LinnWorks ID and how to add Non-sync list and how to remove from Non-Sync List
How to Delete Items from non-sync list from Redback in bulk. (permanently remove the products from the website)