I don't know if anyone already suggested this (probably did)

but there should be a button for borrowing a pet to someone for a quest. Lots of players do that but this way they could have a guarantee that their pet will return to them.

makes sense.

Hmm. I'm not sure how this could be done, but I would certainly love an idea like that. I do lend pets for quests and not getting it back is a concern, especially with people I have not lent to before. 

This would also make it easier for the person borrowing the pet. It is sometimes rather a hassle finding out who you got a pet from.. You have to look through your mail, see who sent you a pet, click the link in the mail (since often people send Nameless pets), then click the Gift button on that pet's profile and type the name of the owner. I get distrcted rather easily and have often wondered what would happen if I typed the wrong name and accidentally sent the pet to the wrong owner. An option like shana5 suggests would eliminate those fears. It would also guarantee that the pet comes back to the owner as soon as possible, once the quest is done, and not when the Lender comes back online.

I suppose it could work with an extra button under Sell on Auction, "Lend for Quest" and after clicking it you would type the name of the Recipient and select the quest the pet would fit for in that person's quest list - I'm just not sure how this would be codewise and if it would be in demand enough to make it worthwhile. There usually aren't too many people active in the Pet Lending thread.