When the TCP connection is disconnected (because the old pod stopped) gRPC's channel will attempt to reconnect with exponential backoff. Each reconnect attempt implies resolving the DNS address, although it may not detect the new address immediately because of the TTL (time-to-live) of the old DNS entry. Also, I believe some implementations resolve the address when a failure is detected instead of before an attempt.
This process happens naturally without your application doing anything, although it may experience RPC failures until the connection is re-established. Enabling "wait for ready" on an RPC would reduce the chances the RPC fails during this period of transition, although such an RPC generally implies you don't care about response latency.
If the DNS address is not (eventually) re-resolved, then that would be a bug and you should file an issue.