Question

what is mrs. higgins talking about when she says: "be quiet, henry. colonel pickering: don't you realize that when eliza walked into wimpole street, something walked in with her?"

Answer 1

Henry is the one who walked all over Eliza by taking over her life. She came wanting lessons in how to speak correctly, which she received in addition to being bossed around by Henry, her teacher. 

Answer 2

What is mrs. higgins talking about when she says: "be quiet, henry. colonel pickering: don't you realize that when eliza walked into wimpole street, something walked in with her?"

She shows concern that her son and Pickering have been short-sighted, and have failed to acknowledge the extent of their task.

I hope it helps, Regards.