Read the characters' dialogues. The game states that there are 3 characters involved in this topic: a girl with tentacles, a girl with horns, and Celica. And a place where no one will see this monster.
If Celica learns to use artifacts, she will be able to resist such things and end such displays of attention. Perhaps she already knows how: pay attention to the button that may appear on the left.
As for this "pet", this is where its functionality ends in the current beta version of the game (0.71.X).