No definite information as to why it's used on the GOP Elephantasscot
A typical Neopagan pentagram (circumscribed): a symbol used in many Neopagan traditions to represent earth, air, fire and water, plus the fifth element of quintessence or Spirit.
Pentagram image from Heinrich Cornelius Agrippa's Libri tres de occulta philosophia illustrating the golden symmetry of the human body. The signs on the perimeter are astrological.
Pythagorean use
The Pythagoreans called the pentagram ύγιεια Hygieia ("health" also the Greek goddess of health, Hygieia), and saw in the pentagram a mathematical perfection.
The five vertices were also used by the medieval neo-pythagoreans (whom one could argue were not pythagoreans at all) to represent the five Classical elements:
ύδωρ, Hydor, water
Γαια, Gaia earth
ίδέα, Idea or ίερόν, Hieron "a divine thing"
έιλή, Heile, heat (fire)
άήρ, Aer, air
Satanists use an inverted Pythagorean pentagram (one point down), often inscribed in a double circle, with the head of Baphomet inside the pentagram. They use it much the same way as the Pythagoreans - after all, Tartaros does mean Hell in Christian terminology (the word is used as such in the Bible, referring to the place where the fallen angels are fettered). The pythagorean Greek letters are most often replaced by the Hebrew letters לויתן forming the name Leviathan. Less esoteric Satanists (LaVeyan types; the ones that exist in abundance) use it as a sign of rebellion or religious identification, the three downward points symbolising rejection of the holy Trinity.
http://en.wikipedia.org/wiki/PentagramMedal of Honor
One source said it's a Blanket of Stars of which the left side would be upside down.
One said, it's not upside down, it's LEANING RIGHT. :)
Huffington Post
edit to add a pic.