Re-rent the clubs again and when it comes time to equip them, put your originals back. The rental period still has a few hours to go.
I had the same problem yesterday and the fix was to replace the rentals before they expired. Unfortunately, the 3 wedges I was trying did expire and I refused the sale offer when they ran out. After returning them I put the original wedges back but that save option wasn't there.
I did the log out thing and when I logged back in I got the expired rental message but still wasn't able to put the originals back, no matter what I did. Lucky for me the free rental was still on so I re-rented the wedges and instead of equipping them, I put my originals back. Problem solved.
I still get the "you have rentals to equip" but I just close it.