That one is gone, but there is a way to get it back sort of. Just go to the bazaar in Wizard City and buy a new robe. There is a huge selection there and a ton of great items. Who knows, you might find one that is even better than the one your pet chewed up!
I recently fed an unwanted item to a pet. There is a warning screen that prompts "Are you sure you want to feed (item name) to (pet name)?" with "yes" and "no" answers possible.
I was in the Warehouse (Level 60 dungeon) and got a boots drop. I thought the stats weren't good, so I fed them to pet. In doing this, I accidentally fed my "Forest Spirits Careful Boots" (drop from oakheart) to my pet instead. I was mad, but I farmed for them again a few days ago and got them back ^-^.
ah im sorry to hear about that :(, but if you want to get another one [possibly a better one] keep doing your quests, you will surely earn something nice :D