Do you mean the search suggestions that appear in a drop-down below the search box as you begin typing your search keywords?
I believe there are three separate things that you may be seeing.
eBay can provide search suggestions based on your past searches; those appear in blue or purple, depending on whether you have erased your browser cache or history recently -- those suggestions can be erased by going to your "Recently Viewed" page and selecting "Clear all". "Hide eBay suggestions" can also hide those, if that option appears (it does not always appear).
eBay also provides generic suggestions that appear as black text, such as "airpods" and "apple watches" when you type the letter "a" in the search box, even if you have never searched for those things. Those can only be hidden by the "Hide eBay suggestions" link at the bottom of the drop-down.
In addition, your browser may be remembering past form data that you have entered in that field -- your past search keywords. These are different than the eBay suggestions; they usually appear in a smaller font, in black. Those can be deleted individually by using the up and down arrow keys to select and then hitting the delete key. Or you can delete all at once by clearing form data from your browser (exact details depend on which browser you are using).
