Do increase Grenade damage on gear work with Strafe Demolition

If I enchant these pants for +Grenade damage, then would the grenades from Strafe Demolition increase in damage? The Hellcat Waistguard makes the grenades from Strafe Demolition bounce so I am unsure about the +damage part.

Unfortunately not, because the effect you are rolling in that screenshot is showing you available primary skills as replacements, and Grenade (capital G) is a primary skill for the demon hunter.

The description for Strafe's Demolition rune uses a lowercase G for "grenade", probably just to describe the visual effect of the rune, but does not in fact fire off an instance of the primary skill "Grenade".