The term 'Bucky B. Beaver's Brand' is a reference to the toothpaste brand IPANA, which was created in 1915 by the Bristol-Myers Company. IPANA was advertised as being endorsed by Bucky B. Beaver, a cartoon character who was featured in the company's advertising campaigns. IPANA was one of the first toothpastes to contain fluoride, and it was popular for many years before eventually being discontinued in the 1970s.