Switch banks and if they ask why, tell them.I accidentally took out my CHL once going through airport security. The one TSA agent looked at it funny (wasn't in Texas) and then ended up dropping my DL on the other side when putting things back in their place. When talking to the TSA agent that recovered my DL he said the CHL would have been fine as it was state issued and heck, he was aware of the background check requirements, it made him more confident I was safe anyway.
Kind of interesting.