Before deleting a web part on a page, it is important to give it a name different from the default one, since you may maintain some Web Parts in the page. This can be defined in Web Part Properties, it appears when you click on the cog wheel, in the BindTuning Web Part menu, on Chrome Appearance section. When you finish it, please click on Save button.
At first, it is required to have the page checked out. Please click on Page tab and then on Check Out:
Then, add ?contents=1 in the end of the page URL and press Enter to navigate to the new URL. See the example below:
You will see another page where all the web parts from the previous page are listed. It is important to give different names to all web parts, since here they are discriminated using those names. Select the web part that you want to delete (on the respective checkbox) and click on Delete.
The web part is now deleted. The list will be updated and that specific web part will no longer appear there. You can select more than one web part, if you have the intention to delete more than one.