What term describes a carved mythical creature used purely for decoration on a building?

The term that accurately describes a carved mythical creature used purely for decoration on a building is "grotesque." Grotesques are ornamental figures that often depict fantastic or exaggerated forms and are commonly used in architectural design to add visual interest. These figures are not typically functional, meaning they do not serve a practical purpose like water drainage, which distinguishes them from other architectural elements.

While gargoyles are also carved creatures found on buildings, they specifically serve a functional purpose by directing rainwater away from the structure to prevent erosion. Fretwork refers to ornamental architectural decoration, usually consisting of intricate, interlaced patterns, rather than specific creature forms. A frieze is a horizontal band or decoration that runs along the upper part of a wall, typically featuring reliefs or motifs, but it does not refer to individual decorative creatures. Therefore, in this context, "grotesque" is the most suitable term for a purely decorative carved creature.