Learn Spanish (Latin America): El comodín no les dio un premio, sino un mejor puntaje. - The wildcard didn't give them a prize, but rather a better score.

We use sino because we are making a direct correction to a negative statement. When a sentence follows the pattern "not [A], but rather [B]," where [B] completely replaces [A], you must use sino. If you were just adding contrasting information without replacing the first part (e.g., "It didn't give them a prize, but it was fun"), you would use pero.

Could we use sino que instead of sino in this sentence?

Not as it is written. You need to use sino que when the phrase following it contains a new conjugated verb (for example, if the sentence said sino que les dio un mejor puntaje). Because un mejor puntaje is simply a noun phrase with no conjugated verb, we use just sino.

Why does "them" translate to les here instead of los?

Les is an indirect object pronoun, which tells us who is receiving the action. The wildcard didn't give the prize to them. If you used los (a direct object pronoun), it would imply the wildcard was literally giving them away to someone else!

Why is mejor placed before puntaje instead of after it?