tile marks

I want to move my shower's glass holder further, so that leaves the old hole in the tile, with a wall plug in it. How do I remove the wall plug, and how do I fill the tile with (beige) filler? Or, what filler do I use? Pictures attached.

Hi, I had my bathroom refurb done including new tiles. Once the bathroom was complete we did not clean the tiles as there was other work happening in the house. We have just got around to cleaning the white tiles, but there are so many marks still visible on the tiles and it looks like trovel...