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

Deleting a button

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

Choose Delete in the drop-down list:

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

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

Publish the site for the changes to appear live.

Tip: check out the article Changing the design of a button to learn how you can adjust your button's design.
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