@tony Do you mean that after redeploying your function and configuration you still observe that it uses the old connection string?
It "feels" like a connection string my be stuck in a cache that survives between deployments.
It depends how you have define the connection string. If you have define it static client the it reuse client instances rather than creating new ones with each function invocation.
But once you have changed the connection string (application setting) and restart your function then the static client should get the new connection string after the restart. Can you restart your function app and see if you observed the same issue.