В DBGrid напротив некоторых строк можно поставить галочку

tblFounds.IndexFieldNames = 'Advertis'

procedure TMainForm.dbgWorkDblClick(Sender: TObject);
begin
  TriggerRowSelection;
end;

procedure TMainForm.TriggerRowSelection;
begin
  if dmFile.AdvertisCount <> 0 then
  begin
    with dmFile do
      if not tblFounds.FindKey([tblAdvertisID.Value]) then
        tblFounds.AppendRecord([tblAdvertisID.Value])
      else
        tblFounds.Delete;
    dbgWork.Refresh;
  end;
end;

procedure TMainForm.dbgWorkDrawColumnCell(Sender: TObject;
          const Rect: TRect; DataCol: Integer; Column: TColumn;
          State: TGridDrawState);
begin
  if DataCol = 0 then
    with dmFile, dbgWork.Canvas do
    begin
      FillRect(Rect); {clear the cell}
      if tblFounds.FindKey([tblAdvertisID.Value]) then
        TextOut(Rect.Left, Rect.Top, 'ь');
    end;
end;

with dmFile, dbgWork.Columns do
begin
  BeginUpdate;
  Clear;

  {check mark}
  nc := Add;
  nc.Width := 14;
  nc.Font.name := 'Wingdings';
  nc.Font.Size := 11;
  nc.Alignment := taRightJustify;
  nc.Title.Caption := 'ю';
  nc.Title.Font.name := 'Wingdings';
  nc.Title.Font.Size := 10;
  nc.Title.Alignment := taCenter;

  {skip определения остaльных колонок}

  EndUpdate;
end;