"iteration"???

I want to understand if an iteration is needed here or not.

discarding king, score is 13.
discarding a queen, score becomes 1 only.

up to you to understand what's going on to get there (you're supposed to solve the task, not us ;) ).

Why not K♣?

one of the queens.

For example.

Starting hand: [A♦ Q♦ K♦ K♣ K♥ Q♥ A♥]
Adding card: K♠

Which card should you discard?

omg... I messed T with A. I'm sorry!
So, i rewrite question.

It isn't sequential. The values of the cards are T=10, J=11, Q=12, K=13.

So T, Q, K is not sequential.

Hmm. From instructions: "Runs: three or more sequential cards of the same suit ..."
T♦ Q♦ K♦ is three sequential cards of the same suit.

They aren't. J♦ Q♦ K♦ or T♦ J♦ Q♦ or T♦ J♦ Q♦ K♦ would be. You're missing a Jack in both.

But T♦ Q♦ K♦ and K♥ Q♥ T♥ is a melds too.

K♦ K♣ K♥ is a meld. Cards in a meld score zero points, so it reduces the hand score.

Why not K♣?

Either of the Queens Q♦ or Q♥.

For example.

Starting hand: [T♦ Q♦ K♦ K♣ K♥ Q♥ T♥]
Adding card: K♠

Which card should you discard?