i think better dont't put anything inside your newborn baby.. specially cloth.
my baby also like that, but it's only if i feed her formula.
once i breastfeed her then i dont't see the whitish milk residue on her tongue..
maybe you try breastfeed?
anyway if still there i tink better dont do anything extreem about it.. maybe try to feed her few sips of water but not too much coz i read that newborn can not drink too much water otherwise they will get seizure..