palate: (noun) roof of the mouth; preference in taste or flavour
palette: (noun) the board used by artists for their paints; the range of colours used in art or makeup; (adjective) used with the word “knife” to describe a tool used by an artist to spread paint
pallet: (noun) a portable wooden platform used for storing or moving goods; a temporary bed, often made of straw; a wooden tool used to shape clay
pallid: (adjective) wan, unusually pale because of illness
A sophisticated palate means you have a preference for elegant food.
A sophisticated palette might mean you use a board truly meant for paints rather than an old plate.
A sophisticated pallet probably means you upcycled some materials discarded from a warehouse.
If you are pallid, you should probably take the day off and not try to be sophisticated.