If the Grappler were say an undetected Giant Octopus or a Froghemoth who first Attacked and then used the Grab Free Action Attack to Grapple, only the first Attack would be vs. Flatfooted AC, the defender gets the Dex Mod to his CMD for the Free Action Grapple Check.
If the creature began with a Standard Action Grapple attack, against the first Grapple Check, assuming the invisible grappler were not detected, the defender would not get his Dex Mod to CMD. The canny Invisible ambush Grappler would probably begin with a Standard Action Grapple on the party straggler rather than with an attack followed by the Free Action Grapple.
After your first attack, you usually then become visible.
If the Grappler had Greater Invisibility, were attacking a Blinded victim, or otherwise enjoyed Invisibility after attacking, usually the Grappler has the Grappled Condition, too, and enjoys none of the benefits except for a +2 CMD. However, White Haired Witches can Grapple without being Grappled themselves fairly easily, and if you are so Grappled by a White Haired Witch under Greater Invisibility, you are in a lot of Trouble!
It seems to me that if instead of using a Free Action Grab Grapple but rather an instant Grapple off of Hamatula Strike, you get to make your Grapple Check vs. Flatfooted AC, since it is not specified that the Grapple is a separate action from the initial attack. But I can also see a GM not allowing that.
