The Purple Heart is awarded to US military personnel who are wounded or killed in action, and was first used in the mid-20th century. The Martian award appears identical to the US medal. About half a million medals were made in preparation for the expected casualties from the planned invasion of Japan in World War 2. With the invasion unnecessary, these medals were stored and awarded gradually in post-WWII conflicts. It is possible that the stockpile still existed in the 23rd century, and these old badges were still being issued.
Previously it was established that Belters, who lived in microgravity, could not endure Earth's gravity. Gunny is going to Earth where she will encounter gravity that is 2.5 times Mars normal. Imagine a 150 pound person suddenly weighing 375 pounds; that is Gunny's position. However the show has been explicit about the fact that Martian Marines train in 1g environments (Earth-like gravity) precisely to prepare for the contingency of doing operations on Earth.