Does Teemo Strategist need to pay Deflect to do the effect? If so, can they choose not to pay Deflect, and what would happen if they don't?

Yes, if you target a unit with Deflect (e.g. Deadbloom Predator), the Deflect cost is incurred once — Deflect is paid per targeting instance, not per damage.

However, you may decline to pay that cost. Under Rule 404.2 and the updated trigger cost rules, players can refuse Deflect costs incurred by triggered abilities. If you decline, the ability ceases to be a Pending Item and is removed from the Chain — it never becomes a Chain Item. This means no cards are revealed and no damage is dealt; the ability fizzles entirely.

If you do pay the Deflect cost, the ability finalizes normally: you reveal 5 cards, deal 1 damage per Hidden card revealed, then recycle.