How do you get rid of the dog?

[123]

It needs to leave

[Reality]

Reported to P.E.T.A.

[Swift-Li]

The puppy from the quest is not your pet. Just let it DIE!

[Zombie Teddy Bear]

Attach it to the gallows!
long live the BEAR!!!!

[Minterfresh]

I want to know too, the dog was forced into my party and I don't see a banish option, same as my kitten starter (keeping), are they locked somehow?

[Tired Gamer Syndrome]

I think you can just banish it by talking to it once its back at camp

[iicycube]

Just make then died then they will spawn in your land again.
then the "talk" will appear.

[noname979427]

Can't you just dismiss them back to the base or something?

So that they can ask you for rock's on the quest board day's later.

[Shard]

Get within a few squares of them, middle-click on them, select talk, then tell them to stay at the base.

[Revi-Dragon]

just "Middle Click" on the Puppy to select the "Talk" option, and then tell it to wait home, and it will go to one of your owned location you own the Deed to, like the Starting Meadow.