Yes.. they will need to claim the bags in a chaos that is Mumbai international, clear customs, do a security check at the gate for the shuttle to the domestic terminal and finally catch the shuttle to the domestic terminal.

At the domestic terminal, they will need to check in again with their bags.. standard procedure.

I had a similar flight last week- DTW-FRA-BOM and 9W 756 to BLR as FRA-BLR was sold out.

Few things- Pls ensure that there is ample time between the connection at HYD. My flight was delayed at FRA due to a technical glitch which made me miss my original connection to BLR. LH DID NOT book me for the next flight (although this was a single booking). I had a few co-passengers with connecting flights to HYD miss their connections as well