One thing nobody has mentioned is that potentially no verbal response at all is warranted but just non-verbal one, like a smile, eye contact and nod while passing by.
The sequence of events was that you made a compliment, and the addressee thanked you for it. All intended information has been exchanged, symmetry in communicative and social terms is now achieved, and there is nothing more to say, really.
Of course what happens next depends on the situation: If you are passing by a co-worker in the office like it was 2019, and simply noticed their nice shirt, you didn't mean to really interrupt their work and start a conversation. If, on the other hand, you finally found the courage to talk to the person you have been admiring from afar for the past 6 months you surely will try to continue from here and add "You are welcome [to talk to me for the rest of the day!]. You know, it really fits with your blue Mohawk" or something similar.
In all reality such a remark is typically made when either the person or the shirt was an incentive to actually have a conversation, so the more natural response would be informed by what the incentive was. "Welcome, I've been looking for something like that, where did you find it?", "Thanks,
it looks really beautiful on you" etc. would be plausible continuations.