I thought it would be a good idea to collect the different chat options with your pet here too, so we can see which rewards can be had from the different answers.
Sometimes your pet wants to talk to you, and you will get a message in chat which looks like this:
Then a small box will appear next to your mini map, click on it and you will be able to talk to your pet.
I got the following Chat option today:
I chose the third option "Did it drop any treasure?" and received a gift from my pet.