Can wearing a tight basketball headband cause damage to ear cartlidge?

Depends. Tight clothing can significantly alter blood flow which can damage any tissue. Short periods are usually not a problem. But if you do this for long periods, often, you may have problems. If the band is tight enough that you notice numbness or tingling or the skin is paler than normal afterwards, then the headband is too tight. Lighten it up! Even tourniquets cannot be in place for long!