This shirt by Japanese artist and animator Hine Mizushima. It seems to depict some kind of bizarre telephone machine, complete with "TMBG" buttons and resident Giant squid. It conveys the message "Zei-Mai Daisakusen", or "Operation TMBG" for English speakers.
The back features the band name in large letters and the Giant squid, who appears to be turning off a light switch. Here's what Hine had to say about her creation on her blog: "Perform your important mission for They Might Be Giants (hopefully after ordering and putting on the T shirt). Make sure it's not bugged by an enemy spy!" Purchase "Squid on Green" from the merch store. There's also a womans' version available.
As a parting bonus, here's Hine's stop-motion animated video for With the Dark, starring that lovable Giant squid.