
flamethrower49 |

Rules as written... yeah. It's a prerequisite. Which makes the grapple feat chain really annoying. Thing is, it's still worth it!
A kind DM might allow you to bypass that requirement though, if you cite the fact that the ape essentially already has the basics of Improved Unarmed Strike. I couldn't get that past my DM for my Serpentine Eidolon, sadly.

Axl |
Technically, ape animal companions have bite and claw attacks, not improved unarmed strike attacks. So, RAW, it would need to take IUS as a prerequisite for Improved Grapple.
However if I was the GM, I would houserule to allow the ape to take Improved Grapple without IUS.

Chovesh |

Here is where I disagree.
You are skilled at fighting while unarmed.
Benefit:You are considered to be armed even when unarmed—you do not provoke attacks of opportunity when you attack foes while unarmed. Your unarmed strikes can deal lethal or nonlethal damage, at your choice.
Normal: Without this feat, you are considered unarmed when attacking with an unarmed strike, and you can deal only nonlethal damage with such an attack.
The “Normal” does not apply to the Ape, and is not the “Case A” for which a new “Benefit:” (Case B) then becomes the norm. The ape already meets the conditions that are the 'Benefit' and therefore the conditions which are a prerequisite for Improved Grapple are already met.
The 'Feat Name' "Improved Unarmed Strike" is simply a (name) 'wrapper' for an ability (do lethal unarmed damage) that must be had in order to use Improved Grapple.

Frankthedm |

Does my APE animal companion need to get Improved Unarmed Strike before getting Improved Grapple, or are they already considered to have it?
They do not have the feat, they must take the feat to meet the prerequisite for Improved Grapple. Otherwise every monster with a grab attack would take the Improved Grapple feat to get the bonus on grapple rolls.