That shelf is most likely installed between tiles. That is, the tiles above and below the shelf provide the support. This is especially critical at the corner.
Your pics are actually too close. The tell-tale factor is the corner.
Removing the shelf can leave a gap in the tiles. This is one of those times where there is no way to remove something without additional work needed after. What work is unknown until the shelf is removed.
Can you remove it without damaging the tile? Maybe, maybe not, this is a situation where surgical removal is needed, but there is no guarantee there will not be damage.
Remove the screws. Use a rubber hammer and rap down on the top of the shelf. Then try under, hitting up. (Wear all the proper safety protection). It may help having someone hold the shelf while you hit it, so it doesn't fall and cause more damage. There are no "tricks" that I know of.
I have removed corner shelves. Filled the gap with sanded grout and sealed the grout. This still left an ugly scar. I covered the scar with a stainless metal shelf that looked more modern. Sealing the edges around the new shelf as well. This was acceptable to the homeowner, but may not be what you are after.
Bottom line here is, it looks as if you will need to find a new suitable shelf or retile that entire area while maintaining the waterproof envelope.