The soldier obviously is invested in Trump's candidacy and the political issues wrapped up in that. Trump will take a hit in the press for whatever he does with the offered gift, if he had rejected it, he would have been called "uncaring about his supporters." By accepting he, and only by accepting it, can Trump give something (tangible) back to the giver.
Imagine having a thank you letter, handwritten, from the president - and your medal back, with remarks of gratitude and appreciation for the thought and trust.
Lots of emotion, all around.