If you counter a spell, does Jhin still get to banish it for his legend effect?

No, you cannot banish a spell with Jhin's legend effect if it has been countered.

According to RiftJudge FAQ #8769 and Rule 425.1.b, a spell that is countered is not considered to have been played. Furthermore, Rule 425.1.a states that a countered spell is cleared from the chain.

The Sequence

1. Playing the Spell: You play a spell and pay its costs. It is placed on the chain.
2. Reaction: Your opponent plays a card (like Defy) to counter your spell.
3. Resolution: The counter resolves, and your spell is cleared from the chain.
4. Trigger Check: Because the spell was countered, it is not considered to have been "played" for the purpose of triggering "When you play a spell" effects. Consequently, Jhin's ability does not trigger, and even if it did, the spell is no longer on the chain to be targeted or banished.

This is consistent with RiftJudge FAQ #9343, which clarifies that a countered spell does not trigger "When you play a spell" effects.