I had the same problem. Firstly i relogged (i had 3star tristana and vayne that game) but mission was still "undone"/notcomplete, so i begun writing a ticket to riot. I recomend you to do it if your problem have not been solved yet. I often write tickets and riot replays pretty quckly. I assume unless you got banned and want to get unban you don't deserve they would be polite and helpful. I write about this because i noticed people tent to make threads instead of geting their "individual problem solver" who is very likelly to be more effective. Anyway I recomend you to write a ticket. Speaking of me my problem has solved by itself, I went to client for a precise mission name and the claim button was there :3.