The Beautiful Fleshy Woman (肉感的な美女) is a unnamed woman who used to work for the Old Yorozuya, taking care of the paper work, finances, etc. Her position is equivalent to that of Catherine's, as explained by Gin in Episode 138.
She has long, pink hair and wears a red cheongsam with black piping. Kagura was so jealous of her assets when she saw her photo that she stuffed 2 mandarin oranges underneath her jump suit. It was Shinpachi who gave her the nickname the "Beautiful Fleshy Woman" (肉感的な美女), which Kagura thought was gross.
She used to work for the Old Yorozuya, and shared their fate being thrown over a bridge into a river by Sakata Gintoki. However, it is uncertain if she survived or not, considering most of the Old Yorozuya survived, as seen in Episode 164.