It's not stated
"Distasteful" isn't any status or descriptor in the D&D 5th edition rules, except in the banishment spell. It's up to the DM.
However, the version of banishment in the earlier D&D 3.5 Player's Handbook (p.203) gives a more elaborate example of what items may be "distasteful", and you might use this as inspiration. It includes things which the target hates, fears, or otherwise opposes; particularly things which it is vulnerable to (examples include weapons made from a metal the creature is vulnerable to, or elements it is vulnerable to); and especially certain individual rare items that this individual especially dislikes.