Officially, you can take your business class amenity kit with you but not the bedding. People do it anyway, which shouldn't be surprising since passengers at Delta Sky Clubs are dumping buffet items into their carry on bags and guests steal insane things from hotels.

The "rule of thumb" for taking items from business class is: if it’s a single-use item or part of a "gift" kit, it’s yours; if it’s durable equipment, it stays on the plane. You are encouraged to take the amenity kit (the pouch containing the sleep mask, socks, earplugs, and high-end skincare samples) and the airline-branded pajamas or slippers, as these cannot be reused for other passengers. You can also take any printed menus or high-end magazines. However, you should never take the blankets, pillows, or duvets, even if they are designer-branded (like United’s Saks Fifth Avenue bedding). Similarly, the noise-canceling headphones, glassware, ceramic plates, and metal cutlery are the property of the airline and are collected at the end of the flight. Taking these "durable" items is technically theft and can result in the airline charging your credit card after you land.