you must add the game as "owned" first,
I think not. At least on the main BGG game page, when you get to the Edit screen (after selection "Collection") you can find the 3 stacked dots in the upper right. Mouse over those dots and see "More Options". Actually click on the dots and be offered "Delete from Collection".
I would have to experiment more with the Collection view from your Profile area to discover how things are there.
There is a big red X on the right side of the item that will delete it.