Pilar has had a simultaneous Fox's Cunning and Owl's Wisdom before, and this is, greater, and not just in the way of +5 versus +4, there is something in it not captured in the measurements.  But she's had +4/+4 before.  It's not that different...

At +5 Wisdom it's very obvious to Pilar that she is lying to herself.  She knows she has done the equivalent of putting on an artifact headband she can't take off, and that's before taking into account the actual artifact headband that she still has, returned to her by Keltham, in her Bag of Holding.

Pilar has had a simultaneous Fox's Cunning and Owl's Wisdom before, and this is, greater, and not just in the way of +5 versus +4, there is something in it not captured in the measurements.  But she's had +4/+4 before.  It's not that different...

At +5 Wisdom it's very obvious to Pilar that she is lying to herself.  She knows she has done the equivalent of putting on an artifact headband she can't take off, and that's before taking into account the actual +4/+6/+6 headband that she still has, returned to her by Keltham, in her Bag of Holding.