Whoever installed this did a terrible job. You're not supposed to put the cover before grouting. The cover should have been removed, grout applied, then the place for the cover carefully cleaned of grout so the cover fits.
In any case there shouldn't be grout where the arrow points. If the cover is put in before grouting, the grout that falls through the holes can't be removed. It's probably stuck in your drain now, which could explain the situation...
The grout that's stuck in these holes is probably holding the cover. You can stick something into the holes, like a flathead screwdriver, and turn it to grind the grout away. Also, since grout is brittle and metal is ductile, you can try to pry the metal off, using the screwdriver as acrowbar, or gently tap it with a hammer.
If you bend the cover, you can always get another one or hammer it flat on a workbench. If you use a screwdriver as a crowbar to pry it off, do not use the tiles as support, they will chip.