Hello, thanks for the great question. I’m sorry to hear that your buttons are not appearing the same on the front-end as they do in the editor.
One thing I notice is that not only are the button backgrounds missing, but the text also has a heavier weight. This leads me to think that you may have some custom CSS on the front-end that doesn’t match the CSS coming from BoldGrid. Two questions:
Do you have any Custom CSS rules defined in the Customizer?
May I ask which theme you’re currently using?