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Adjective: indelicate  in'de-lu-kut
  1. Bluntly inconsiderate of others' feelings; lacking social sensitivity
    "She asked indelicate questions about their finances"; "indelicate questions about our relationship";
    - tactless, untactful
     
  2. In violation of good taste even verging on the indecent
    "an indelicate remark";
    - off-color [US], off-colour [Brit, Cdn]

See also: inconsiderate, inelegant, tasteless