erase pen from Drawing app with transparent bg

Hi,
I have a simple drawing app, using the LineTo command to allow users to change colours and draw what they will.
As the background I have a picture.
So the user's drawing is in a movieclip on top of the background picture.

My question is how to let the user select eraser, and draw over any of their lines with an invisible line - therefore erasing their previous line. Simply to erase a line in the same way you would with a real eraser.
The problem here is setting the colour to 'invisible' because if I had a white background I could just set the colour to white - however I don't. I have a picture as a background, so I need to have an invisible colour that will overwrite the other lines...

I have an undo button working, and a clear button. but I need to get this eraser working too.

Does my question make sense?

Any ideas?

Thanks.

Have you tried setting the alpha to 0?

yeah, I tried setting the alpha to 0, but then it didnt overwrite the other line.
It was completely invisible...