Piece of deal (3” x 15” x 1”) has been stuck to plasterboard in bathroom presumably with ‘no nails’ how can I remove this?
I've never heard that usage of "deal" before either. Is it stuck to the wall or embedded? If it appears to be stuck on, maybe there are some screws (hopefully into studs) that you are missing. Anyways, as Jeff suggested in comments, get a pry bar and some shim or scrap wood to pry against (avoid prying on the plaster directly or you will make dents) and see if it will come off. As you pull on it, any fasteners may become apparent. Otherwise just apply pressure on all sides and see how it comes. If it was put on with a strong construction adhesive or such, you may end up pulling off some of the wall's surface, which will necessitate some patch work.
I've seen construction where wood was embedded in the wall because they knew that's where sinks or cabinets would be mounted. You can always skim over that if you make different choices.