Determine if you have a state statute that authorizes "Pre-need" burial contracts. (If you cannot locate it easily, call your state funeral directors association.)
The statute will spell out who is to do what and under what circumstances and they vary from state to state. If your bank is named as the trustee, it's appropriate that you hold the time deposit. Otherwise, it is not.
All of those I'm familiar with do require that a specific funeral home be named, so it seems a bit odd. Sometimes, banks just make stuff up...
"Never take advice from the other guy's lawyer." Me