It's been very long since I played this quest. Like JS/Slicer : agito --> JS stands for J-sword which is a katana.As far as I can tell from your picture, the Japanese katakana always matches the left part of the weapon.
HA would probably stand for Halbert. Maybe we should translate the names from katakana to English to make it more clear. As for the items that are not on the allow list, could you report the items that made the message appear so we can take a look at them? Also, if you give me your guildcard and the slot of the character you did this quest on, I can give you another Type weapon to make up for the lost one.