Nancy controls a Illusory Gains enchanting Alice's Wall of Ice. Alice plays Profaner of the Dead, and after Illusory Gains takes control of it, she decides to exploit the Wall of Ice that was just returned to her.

Does Profaner of the Dead trigger to bounce the remainder of Alice's board?

Yes, it does. (Assuming Alice doesn't control anything else with toughness 7 or greater.)

A creature was sacrificed to Profaner of the Dead's Exploit trigger, so the Profaner has exploited a creature, which triggers its second ability. Nancy currently controls the Profaner and will therefore control the trigger, which means that the ability will return all creatures with less than 7 toughness that Alice controls to their owner's hand.

Note that sacrificing for Exploit is optional; a much better course of action for players in Alice's situation would normally be to choose not to sacrifice anything.