Is operating relay with 3.3V instead of nominal 5V harmful?
Supplying the relay coil with 3.3V instead of the 5V it expects may make it less likely to close or may make it close slower. That could lead to arcing between the contacts. Other than that it shouldn't be an issue for the coil side of the relay.
However, you mention that you're driving it directly from the output pin of your Arduino. That will fry the arduino sooner or later, it is not built to supply the current needed by a relay coil.