With Teemo Strategist, how many times does he need to pay Deflect cost for his ability?

Based on the official FAQ for Teemo, Strategist, you pay the Deflect cost only one time, regardless of how many Hidden cards are revealed or how much total damage is dealt.

Ruling

Teemo, Strategist's ability creates a single instance of targeting and deals damage from a single source. Because Deflect is paid per targeting instance, you only pay it once.

Sequence

1. Declare: You declare you are using Teemo, Strategist's ability (triggered by defending).
2. Target & Pay: You choose an enemy unit as the target. If that unit has Deflect, you must pay the Deflect cost at this time.
   • Note: The Deflect cost must be paid before flipping any cards; you cannot see the results first and then decide whether to pay.
3. Finalize: If the cost is paid, the ability is added to the chain. If you choose not to pay the Deflect cost, the ability does not go on the chain and you do not flip any cards.
4. Resolve: Once the ability resolves, you flip the 5 cards and deal damage based on the number of Hidden cards revealed.

According to Rule 735.1.c, Deflect is a mandatory additional cost applied "for each time they choose me." Since Teemo's ability chooses the target only once, the cost is only applied once.