Ink of Squid Pro Quo is a mysterious item that is mentioned back when Problem Sleuth checked the FAQ for help with the diplomacy situation, it recommended sharpening the Tectrix of the Arbitor and obtaining the Ink of Squid Pro Quo if you were going to legitimately complete the negotiation. Its actual location is in the speakeasy, as the hatless man acquires the Ink before going to the dollhouse and ending up with DMMK. It then finds its way into PS's jacket pocket slot.
When Problem Sleuth uses Sepulchritude, the true form of the ink is revealed - it is the innocuous double of Tectrixcalibur's scabbard. Sheathing the blade covers it in ink, making it similar in use to ammunition due to the ink "meter" shown while Sepulchritude is active.
Since it is a pun off of the phrase Quid Pro Quo, which means that one receives something for doing something in return, it may or may not be applied in that manner. It is also rather ironic in that Problem Sleuth obtained the ink with no effort, it having merely fallen next to him.
It, or a bottle very similar to it, appears in Jack Noir's study. How it got there is currently unknown, although it is more likely just an offbeat reference than some sort of time shenanigans. Spades Slick also has a bottle, albeit with slightly different artwork. It is when describing OPERATION REGISURP to Karkat.