On rotation for takeoff the crew heard a noise. As landing gear retraction was normal and the aircraft continued to operate normally the flight was continued. The aircraft had reached about 220km from Darwin when the crew were advised by a company ground engineer that a section of main gear tyre tread had been found on the runway. The Captain briefed the crew for a possible emergency landing and the flight continued to Brisbane where emergency services were put on standby. A safe landing was made and the aircraft taxied to a parking bay where investigation revealed that the right hand inboard tyre tread had separated, causing damage to the landing gear door clamp. The tyre was a level 6 retread (having been retreaded 6 times), the occurrence being similar to earlier problems with this make of tyre. The company removed all retreaded tyres above the level 4 retread status for inspection.