The first use of "Chimo" as a greeting is in Drage 1748, in Hudson Strait: "The Person in the Canoe... shewed a Piece of Whale-bone, repeating Chimo, and moving his Left-hand circularly upon his left Breast..." Andrew Graham in 1768 wrote that the Eskimos "rub their breast with their open hand, calling in a pitiful tone, 'Chimo! Chimo! which is a sign of peace and friendship. Hearne records "Tima" in 1795: "Tima in the Esquimaux language is a friendly word similar to 'what cheer.'" Edward Chappell in 1814 wrote that "Chymo" meant to barter.
These words each derive, in my opinion, from words that have their own discreet meaning, but in this context of being used as a greeting they have merged. George Back (1836-37) suggested as much when he referred to the men he met "vociferating their accustomed 'Tima' or 'Chimo'..." And McTavish in the 1880s wrote, "I bade the majority of the Esquimaux 'Timah,' generally written as 'Chimo'"
Taima (the modern correct spelling of tima - teyma - timah) today means - that's all, that's enough, it's over.
Chimo (which I think traditionally was pronounced Saimo - like Sigh-moe) comes from a root "saimak" which means blessing or peace. Saimaqsaiji means peacemaker. Saimati in northern Quebec and southern Baffin is "flag" - because after conversion Inuit stuck white flags into the snow beside their snowhouses to show that they were Christian and therefore peaceful. The phrase "saimugluk" (used between two people) today is always accompanied by a handshake, but derives from the same root, so it can be thought of as once meaning "Let's be friends," "Let's be in peace."
So the Taima and Chimo of the early white explorers and traders converged. The meaning was one of friendship and peace, with overtones of barter at the time.
None of this helps us understand "Mannik toomee."