Answer:
Foot-in-the-door technique.
Step-by-step explanation:
The foot-in-the-door technique is a compliance tactic that involves getting a person to agree to a modest request so that, in the long game, they agree to a large request. In this case, the approach in the example is a Foot-in-the-door technique given that they first made a small request (wear a button) so that, after some weeks of wearing that, they accept the large request (adopt a dog).