Question about saying no to requests

We just started using buttons in our house. Two dogs household, sofar they know “snack”, “pet me” and “outside”. The thing is that they looove the snack button. They’ll ask for one over and over again. My partner’s solution was to remove the buttons when we didn’t want them to have treats anymore but I thought it would better to tell them they can’t have anymore treats. Is it better to take away the buttons or teach them that they aren’t going to get something who they ask. What would be the best course of action?