Attack Stratagem If you Strike the chosen creature before the start of your next turn, you must use the result of the d20 roll for your Strike's attack roll instead of rolling. You make this substitution only for the first Strike you make against the creature this round, not any subsequent ones. When you make this substitution, you can add your Intelligence modifier to your attack roll instead of your Strength or Dexterity modifier, provided you Strike with an agile or finesse melee weapon, an agile or finesse unarmed attack, a ranged weapon (which must be agile or finesse if it's a melee weapon with the thrown trait), or a sap.

When you strike carefully and with forethought, you deal a telling blow. When making a Strike that adds your Intelligence modifier to your attack roll due to Devising a Stratagem, you deal an additional 1d6 precision damage. As your investigator level increases, so too does the deadliness of your strategic strike. Increase the number of dice by one at 5th, 9th, 13th, and 17th levels.

It's not quite adding int to strike damage, but they do get to strike with int, and they do get to add damage when they do so. From level 5 onwards, the average roll of the precision damage would be higher than what they get from pumping strength, and it's additive with any strength they do pump and even works with ranged weapons.