I wonder why you think it was not a brass knob. Please let me know if you have some reason for this, because I think that is the correct answer.
You can find this in Chapter 8 of the book. Tom tries to give Becky the "brass knob from the top of an andiron." This is his most valuable possession and he wants to give it to her as a token of his love.
However, she is really angry at him because she has just found out that he has been "engaged" to Amy Lawrence and she will not accept it.
So... is that the problem -- are you supposed to find something that he gave her and she accepted?