To hide a listing, while in list or gallery view, hover over the listing pic, then click the red "X" button that appears in bottom right corner of pic.
To see/clear/export hidden listings, see Settings > Hidden Listings.
By default, this works on ebay.com. Add more eBay sites in Settings > eBay Domains.
Hidden listings stay hidden across multiple visits to eBay sites you have configured. The list also is stored in your browser, no special permissions required.
