If the bitumen has been softened though, this will just result in more treacle-coloured gunge coming up. You can't fix this with further extraction if that's the case, the only way to reduce it would be to let it dry and then bonnet, or minitex ideally, with something that won't loosen up the already dissolved bitumen.
Might be quicker, easier and cheaper to shift a filing cabinet and nick the tile from under it.