Verified answer

Ulquiorra vs. Grimmjow happened in episode 164 and he wasn't sent to some animal world he was placed in a Caja Negacion, which just sealed him off for a few hours. Before that Ulquiorra and Ichigo faced off, Ichigo lost, Orihime got beat up by Menoly and Loly (the two female arrancars), then was saved by Grimmjow as compensation for giving him his arm back. Grimmjow then asks for another favor, which is to revive Ichigo, and he does come back. Ulquiorra comes in, he and Grimmjow fight, and then Ichigo vs Grimmjow begins. 165 and 166 are Ishida and Renji's fights and 166-167 are Ichigo vs Grimmjow.

The episode where Ulquiorra was banished into another space by Grimmjow was probably Episode 165. I'm not sure of the details at that time but if I remember correctly Ichigo had been fighting Ulquiorra and got hurt badly, them Grimmjow took Orihime to Ichigo so that she could heal him so he could fight against Grimmjow...

I think that was it.... I'm not sure what was going on with the other characters and I don't want to write more in case I reveal something that you havn't seen yet.

I hope I was of help ^-^

Episode 165:

The Murdurous Intent Boils!

The Joyful Grimmjow.

Ulquiorra appeared while Inoue is healing Ichigo. Ulquiorra and Grimmjow fought a litte and he used the Caja Negacion to send Ulquiorra to other Dimension so that he wont bother their fight. Grimmjows right arm is badly wounded from defending against Ulquiorra's Cero, so Ichigo ask Inoue to heal his arm too.

And as their fight began, Grimmjow ask Ichigo why he's there at Hueco Mundo, Ichigo answered to save to Inoue, then Grimmjow ask him again "Why didn't you take her the moment you saw her?" and with "Are you realxed seeing her unhurt?! Or I bet you didn't even wonder what was going on inside her." and fight goes on.

Hmmm, I'm not pretty sure about my answer.

It was in ep. 165 "The Murderous Intent Boils! The Joyful Grimmjow"