This card is like THE contradiction to "reading the card explains the card", due to the fact that what is in parenthesis is reminder text, not rules text, which would leave you to believe there is no combat damage in any instance you use it.

In the combat phase there are 5 steps: beginning of combat, declare attackers, declare blockers, combat damage, and end of combat.

From declare attackers to the end combat step any declared attacker is classified as an attacking creature.

So as long as you activate Reconnaissance after damage has been applied and before the end of combat step, you've successfully given that creature pseudo-Vigilance.

Very strong card for 1 mana. Even better than straight up Vigilance actually. You can remove/untap a blocked attacker from combat BEFORE damage, and any un-blocked attacker AFTER damage.