A few months back, I removed some people from my friends' list but I discovered I was still on their friends' list as they were able to send me moogle mail (to which I couldn't reply to because they weren't on my friends' list). My suggestion would be to make the removal of a friend two-way, as in... if you remove a friend from your list, you'd automatically be removed from their list as well. Yes, you could block them but sometimes these things aren't enough to warrant a block.
Quoting this because it's especially relevant with how SE is trying to evolve the social aspects of FFXIV.
Some other/similar issues
People not on your friends list but have you on their friends list can...
• Teleport to any estate you're associated with (personal, FC, apartment)
• Moogle mail you
• Teleport to the nearest aetheryte to you if you're a new adventurer
It's not mutual because you don't have them on your list so you are unable to do the above in return.
(FYI, all of the concerns pertaining to this issue voiced here are relevant.)