It's hard, and I've never seen it done correctly, in the sense that it's the way I was taught it should go:
During slow games, once the players are not writing down their moves anymore because they are close to a game control, the arbiter should write down the moves as well to help with reconstructing the game after a flag falls (say to check if the 40th move is reached), or for claims like this. He can do so as well with blitz games, or appoint a temporary assistant to do so for him. It's just not usually done.
So you can stop the clocks and ask the arbiter to start recording moves, or appoint an assistant. In theory I think he should do that, and then when a threefold repetition occurs after that and you claim, the arbiter can check your claim using his notes.
But in practice, I think most arbiters will be too busy and too unfamiliar with these sort of rules to do that.
And of course, if you get the claim wrong, the opponent gets 3 minutes extra on the clock. Pretty hefty in blitz.