Here's what happened.

On the outbound, the ticket counter agent printed the baggage tag for the IAH-LGW segment, then hand wrote the AUS-IAH information. The baggage made the trip without incident.

On the return, the LGW agent took about 10 minutes to hand write the LGW-IAH-AUS information on green baggage tags. At IAH, the baggage handler told us we had to go to the baggage desk inside the Intl baggage claim area to have the IAH-AUS information re-printed. Made me wonder why the LGW agent even bothered.

But everything made it there with little fuss, so things worked out.