If you have the source code for Controls.pas, find a procedure of drawing WMNCPaint for THintWindow and in procedure call DrawEdge add a flag BF_MONO.
The changed code put in a folder with the your project.
procedure THintWindow.WMNCPaint(var Message: TMessage); var
R: TRect; begin
Canvas.Handle := GetWindowDC(Handle); with Canvas do try
R := Rect(0, 0, Width, Height);
DrawEdge(Handle, R, BDR_RAISEDOUTER, BF_RECT or BF_MONO); finally
Canvas.Handle := 0; end; end;