To not care/give a fig is defined by the online Cambridge Dictionary as "to not be at all worried by or interested in something." Like not giving a hoot. Okay, okay; I took out the "not" for my etegami, and that version of the idiom does not seem to exist in the real world. Call it artistic license. :)
Etegami (e= "picture"; tegami= "letter/message") are simple drawings accompanied by a few apt words. They are usually done on postcards so that they can be easily mailed off to one's friends. Though etegami has few hard-and-fast rules, traditional tools and materials include writing brushes, sumi ink, blocks of water-soluble, mineral-based pigments called gansai, and washi postcards that have varying degrees of "bleed." They often depict some ordinary item from everyday life, especially items that bring a particular season to mind.