Clogged head
Sounds like a clogged head. The software cleaning tool (in the printer options) can only do so much - it only tries pushing more ink through to blast the inkjets clean. The holes are probably solidly blocked and pressure is building behind the inkjets. After the printing has stopped, the in then oozes out slowly through the clot and forms a large droplet on the underside if the head. This slowly dries to a treacle-like consistency and scrapes accros the paper on the next print job.
This usually occurs when the printer gets used infrequently (less than once a week) or if you've been refilling the cartridges.
Lexmark ink is expensive (£40+ for a full set!!!), and the combined scanner is a bonus, but try binning it and changing to another brand of printer and separate scanner.
Try a printer with separate ink tanks (if you run out of magenta - you only replace magenta) These ink tanks normally fit into a removeable print head which makes manual cleaning easier.