Removing ceramic built-in toothbrush holder

No experience, I'd take a diamond blade grinder and cut grooves then bang with a hammer. It will snap in the grooves. Not sure what you'll find behind but chance it will be a long porcelain come or bolt. There will be a spot left.

You will find a hole spanning the 4 tiles the thing covers.

Listen to wife
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The time to remove the unwanted tooth brush holder was when you were going to re-tile and not a day sooner.
Now look what you have.

dj3 said:

The time to remove the unwanted tooth brush holder was when you were going to re-tile and not a day sooner.
Now look what you have.

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I don't understand how your comment is supposed to be helpful ?

Anyways, i'm just changing the sink and not the wall and tile so can't wait for the proper time.

Tiny nails and screw holes are the easiest to fix. You can use a putty knife to fill them with spackling or wall joint compound. But you should allow the area to dry, then you can sand lightly. But anything larger must be covered with a bridging material for strength before the patching compound can be applied. For big holes, like in your case, you can bridge the gap with a piece of adhesive-backed fiberglass mesh. I love this ceramic toothbrush holder, btw. I would like to have one, instead of plastic holders. My dentist (Top Thousand Oaks Dental Care | Full-Service Dental | Thousand Oaks) said that I need to change the toothbrush holder once in a while, that's why a ceramic one would be great.

Astora said:

Tiny nails and screw holes are the easiest to fix. You can use a putty knife to fill them with spackling or wall joint compound.

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Thanks Astora. I've been waiting for your advice since January 2020 !!!! Just kidding. Thanks.