You're correct. Cards are always kept whether you want them or not. It's the item that costs 2 extra ads to keep.
Has it been changed over the last year or so?
The wiki still says:
Ads Service 5 Begin Unslotting Process
+ 2 For each card removed
+ 2 If you want to keep the remaining item
CitationAnd no matter where I look on the Animus website I can't find the list of donation services.