According to Mrs. Higgins, what “walked in with Eliza?” What do Higgins and Pickering mistake her to mean? What does she actually mean? (Act 3)

Pickering thought she meant Eliza's father walked in. Mrs. Higgins actually meant that she walked in with a problem and it was not being passed off as a lady. She says the problem is what the two men are going to do with Eliza, once their stupid experiment was over.