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 are traditionally displayed as a question mark. For nearly all the Monsters, the community has already found their hidden likes, and they are shared here on this wiki on a Monster's page.
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.