I haven't played destiny in a while so I'm not sure if this is normal behavior but I've cleared the raid on one of my characters and I don't have the ability to claim the reward.
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Hope you get this in time. I had the same issue. You need to collect the Triumph from your character's Triumph page, otherwise it won't be updated on Bungie.net. Why? No clue. It is an incredibly dumb mechanic and screws Bungie out of a bunch of money since a good amount of players didn't understand this. This worked for me. I hope it works for you too.
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You gotta buy it dude