In most of the blocks, a button is a separate element that you can delete without affecting the block as a whole.

Deleting a button

1- Hover over the button in the block and click on the three dots:

 2- Choose Delete in the drop-down list: 

3- If you have a couple of buttons in the row, hover over the buttons and click on the "gear" to access the element settings: 

4- In the pop-up window click on the basket icon to delete the needed button: 

3- Publish the site for the changes to appear live.

 Tip: check out the article Changing the design of a button for the customization options available in a button.