Martin Rickett - PA Images / Contributor Costco said that it will honor its contract with My Pillow as other retailers cut off the brand. The retailer is showcasing My Pillow at "special events" throughout the end of February. Visit Business Insider's homepage for more stories. Costco will continue selling My Pillow products despite the CEO's support of former President Donald Trump's false claims of election fraud that have lead many other retailers to drop the brand.