Edit:
I went back on a previous save and left Mantis at the Hive and I still got the Ivy quest. The only thing I can think of at this point is you must have somehow messed up on your conversations with Ivy. Try redoing your choices with Ivy and be as patient/understanding as possible and see if that fixes it.
Mmm... i don't have this stuff... i've been as nice as humanly possible with Ivy/Yuna, still no icon. I'm generally playing a do-godder path. I took mantis back.
EDIT: Does it lead to the cave scene with Ivy? I've been there. But i don't remember how.
EDIT 2: Ok, i had that icon, it just didn't stick with my mind. If it helps my key-choices with Ivy should have been those:
- I killed the decayed and saved her
- I stopped the fatso from killing the girl slave when ivy wanted to meet MC in Zeta.
- I at the mutants bunker dormitory i didn't press ivy, i joined hands with her then i banged Fang.
- I took mantis away from the hive (but this doesn't seem to be important)
- I was cool when speaking with Ivy at home during the night visit.