Refurbishing lcds must always be done in a 'clean room' what I mean by this is a room built to a specific requirement that doesn't contain dust, microfibres etc.
These small dust free rooms are a good start and definitely helps compared to doing it in a normal room, doesn't matter how much you clean, there will always be dust and fibres in the air unless you have a clean room or portable clean room.
Till you do this, you won't be able to refurbish without dust under your screens. :-)