[MAXIUM]

Solución:

Código Delphi [-]
Uses 
    IdCoderQuotedPrintable, StrUtils;

function DeleteUTF8ControlStrings(Text: String): String;
var
  Encoded       : String;
  Dump          : String;
  StartPos      : Integer;
  EndPos        : Integer;
begin
  Encoded:='';
  Dump:=Text;
  while Pos('=?UTF-8',AnsiUpperCase(Dump))<>0 do
  begin
    StartPos:=Pos('=?UTF-8',AnsiUpperCase(Dump))+10;
    EndPos:=Pos('?=',AnsiUpperCase(Dump));
    Encoded:=Encoded+Copy(Dump,StartPos,EndPos-StartPos);
    Dump:=Encoded+Copy(Dump,EndPos+3,Length(Dump)-(EndPos+2));
  end;
  Result:=Trim(AnsiReplaceStr(Encoded,'_',' '));
end;

function MailsGetSubject(Subject: String): String;
var
  Decoder        : TIdDecoderQuotedPrintable;
  TextAnsi       : String;
begin
  Result:=Subject;
  if Pos('=?UTF-8',Subject)<>0 then
  begin
    Decoder:=TIdDecoderQuotedPrintable.Create;
    try
      Result:=DeleteUTF8ControlStrings(Subject);
      Result:=Decoder.DecodeString(Result);
      TextAnsi:=UTF8ToAnsi(Result);
      if Length(TextAnsi)>0 then Result:=TextAnsi;
    finally
      FreeAndNil(Decoder);
    end;
  end;
end;


procedure TForm1.Button1Click(Sender: TObject);
Var
    Asunto: String;
Begin
       ...
       ...
       ...
       Asunto:= MailsGetSubject(IdMessage1.Subject);
       ...
       ...
       ...
End;