The D Gates are actually slightly closer to Terminal 3 than Terminal 1. You'll need to take a tram to reach the D Gates regardless.



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Just to be crystal clear, the American Airlines counter is located in Terminal 1. As such, your plan to use parking at Terminal 3 won't work if you're checking bags or you need to speak to airline personnel before passing through Security

But if you're checking in online and only have carry-on bags, the other folks are correct. TSA won't care if you show up at Terminal 3 for your flight out of the D gates.