When selling all the savicite needed to Beatrice right after you meet her immediately(use the "All" option), she forgets to give you the scarf. Even as she leaves, she will not give you the scarf.
That's why I said "selling all the savicite needed to Beatrice right after you meet her immediately", and pointed out the "All" option as this being the case. I already found the workaround, but it is still a bug that can cause players to lose out on an item they may not even know exists, or will think it is removed.
When selling all the savicite needed to Beatrice right after you meet her immediately(use the "All" option), she forgets to give you the scarf. Even as she leaves, she will not give you the scarf.