No - you don't have any control over what ebay display on their Home page.

There are two ways I can think of: 

1. Don't go to the home page. Bookmark a different page such as your watching list if you're a buyer or the seller hub if you're a seller. 

2. Some ad blockers can remove annoyances like this. See if yours has a feature called "block element" or similar. If so, use this to block the outer rectangle around the live stuff.