Ohio State is probably going to win this one. I laughed at first, and figured the claimed mark was not distinctive enough to qualify as a trademark. I figured if OSU was to have any success, they would at least have to claim colors, or a specific font. But it looks like I was wrong.
The USPTO has already granted a registration on use of the mark "THE" in connection with phone chargers and cables. No issue was raised regarding the distinctiveness of the mark.
More importantly, the USPTO has already allowed an application for the use of the mark "THE" on clothing, including hats and t-shirts. That application was filed by Marc Jacobs Trademarks, LLC back in May of this year, and it was allowed on July 25. On August 6, though, that application was withdrawn from publication by the USPTO for further review, and Ohio State filed its application on August 8. I expect those events were connected, and that OSU is trying to claim prior use and take the mark -- or maybe buy the mark -- from Marc Jacobs Trademarks.
Either way, it looks like the Office does not care whether the mark is distinct enough to actually designate a source. I suppose they will just let that be sorted out through litigation.