After you pull the jars out of the canner, let them cool overnight. Then take the bands off and check the seal (I usually just make sure the lid is indented).
Leaving the bands on is not good. For one thing, they last longer if you remove them and dry them. If you leave them on, they can rust and become impossible to remove. It is also possible for jars to unseal, and if the ring is still on, it is possible that the jar will reseal itself with changes of temperatures.
I just haven't been the same
since that house fell on my sister.