A Mystery Like is a Like that isn't shown in the monster's Likes menu. The last of the four (or in a few cases, five) items in a monster's Likes menu is traditionally displayed as a question mark. For nearly all the monsters, the community has already found their hidden likes.
When a monster is relatively new, this like might not have been discovered yet. Try finding it yourself by buying or selling decorations. So far, aside from the Mystery Likes from Single-Element Rare Monsters, hidden likes have always been decorations rather than monsters.