In the link of the OP here Our Lady did not say to St. Catherine Let us design the medal with a round peg in a square hole. She showed in her vision to the Saint herself, Mary as standing upon a globe, crushing the head of a serpent beneath her foot. She stands upon the globe, as the Queen of Heaven and Earth. Her feet crush the serpent to proclaim Satan and all his followers are helpless before her (Gn 3:15). .
Not a round peg in a square hole. Which is defined as a idiom, with its graphic image of something that cannot fit, dates from about 1800.
Here is the globe you are speaking of. Notice the half dome firmament above and below.
