True. Definitely do not think Tywin would have thought that she was Arya Stark. However, he could tell she was well educated, and had all the proper mannerisms of a Noble girl. Knowing his character, I’m a little suspicious as to why he did not inquire further, but most likely he was too preoccupied to really take the time. Most likely he thought she was from a low noble house that didn’t have much influence in the north if anything. But I feel that it’s well within his character to have looked harder. Is she was a noble girl from a major or semi-major household, he definitely could have used that somewhat to his advantage. Either way while it makes sense as to why he did not look harder, I find it difficult to believe Tywin would overlook any potential benefit to his cause, especially when it’s easy enough to get the information in a convenient manner.