Does Amateur recital remove its counter with not so fast?

Yes, Not So Fast can counter Amateur Recital if the ability targets a unit friendly to you.

Explanation

According to the RiftJudge FAQ #8771, abilities that require a player to select a specific unit to move count as "choosing" that unit, even if the word "choose" does not appear in the card text.

Because the triggered ability of Amateur Recital ("you may move a unit at a battlefield to its base") requires you to select a unit, and if your opponent uses that ability to target a unit you control, the interaction meets the requirements for Not So Fast:

1. Enemy Ability: The ability belongs to an opponent.
2. Choosing a friendly unit: The ability is selecting a unit you control (which is "friendly" from your perspective).

How the Interaction Works

1. Trigger: Your opponent activates the ability of their Amateur Recital and selects your unit as the target.
2. Chain: The ability is placed on the chain.
3. Reaction: You play Not So Fast in response.
4. Resolution: Not So Fast resolves first, countering the ability of Amateur Recital. Per Rule 425.1.a, the countered ability does nothing and is cleared from the chain.