Filling a screw hole in tile

[NorthernLights811]

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.

 

[footprints]

One answer is to just put a screw in with a screw cap, grey, white, beige, chrome mirror screw, whatever you like.
Do not try to pull the plug out if avoidable it may bring some tile with it. I normally find a bolt or rod just a little smaller than the plug dia and use it to tap the plug under flush with a hammer, then use some grout.

 

[NorthernLights811]

I typically push the plug further into walls, but I am no expert so I thought I'd ask.
The solution with the screw and cap is a good one, thanks.
Can I get grout in the colour of my tile at all? I wonder if I don't get the right colour it will look off.

 

[JohnD]

put a hook there.

 

[NorthernLights811]

put a hook there.

Nice! I might just do that actually.

 

[footprints]

Looks grey in your picture you can get it but usually only big bags.
Try a search for.
craft shop grey grout
Some came up in smaller bags one on Amazon.
https://www.amazon.co.uk/Mosaic-Gro...ofessional+Mosaic+Grout&qid=1588682179&sr=8-1

 

[NorthernLights811]

Looks grey in your picture you can get it but usually only big bags.
Try a search for.
craft shop grey grout
Some came up in smaller bags one on Amazon.
https://www.amazon.co.uk/Mosaic-Gro...ofessional+Mosaic+Grout&qid=1588682179&sr=8-1

Thanks for the suggestion and link.
I think I'll go with the hook as I could use one there, and didn't even cross my mind.