Following is related with OWE ticket handling.

I forgot one thing.
BA said, they wanted to charge handling fee for BA-issued e-ticket, when I tried to change date of a CX segment.
Because of BA's e-ticket system's limitation, they need to re-issue an e-ticket to change flights other than BA (CX in this case).
So they wanted me to pay e-ticket re-issue handling fee(25 GBP?).

CX charges handling fee for non CX-issued ticket. But, they don't charge date change handling for other airlines' segment when ticket is issued by CX.

At last, because of I needed a routing change, I paid rerouting fee(125USD) and non-CX issued ticket handling fee for CX.