var 
  Gif:TGifImage;
  PaletteIndex : byte;
begin
  Gif := TGifImage.Create;

  // ... load your stuff here ...

  // TGifImage has an Images property,which is probably only interesting if you're dealing with animations,so just take the first image.
  PaletteIndex := Gif.Images[0].Pixels[0,0]; // palette index for top-left pixel 

  // Now,to get the actual TColor for that pixel,you could do this:
  Self.color := Gif.Images[0].ColorMap.Colors[PaletteIndex];

end;