Giving her the taxi fare struck me as a power move. Like, it's all nice and polite, but it's saying "I'm the one who lives with her, I'm the one who pays for her taxis, she is mine, you are just an acquaintance so don't try to do anything that looks like taking responsibility for her".
The fact that the very next step the girl moves on to is to find out what Iori's income is - so she knows what goal she has to surpass - means the message was sent and received.