Try turning the bump map off. I know it's from the OOTB library, but that's not an appropriate bump map for a tile effect anyway.

What would you use as the alternative?

A proper tile bump map would have the grout lines black and the tile areas white (like the attached). But that's not really the shininess; it's a shortcut to make your rendering more appealing. To affect the shininess, you would different levels in the reflection and glossiness channels. The grout would need a different material (with different physical and material properties) than the tiles.
In Max (for example), you have the ability to control the alignment, scale, and repeat of each map individually for each channel of the material. I'm not certain how much control you have over the alignment of those textures in Revit, if any at all. You might want to start by duplicating your tile map settings (not the colors) in the direct & oblique reflection channels first. You're then controlling the level of reflection with the color of the grout in those maps. Duplicate to the bump channel if you're feeling adventurous.


I would most likely still omit the bump map in Revit and tweak the reflection levels a bit without a map (generally everything has more oblique reflection than direct) and call it a day.

You can set an image map for the reflections as well. That sounds like what you need to keep the tile glossy and make the grout matte.

Try to bump up render settings because in generel the quaility is far from perfect, see reflections on a sofa or a wall. For a bump map you can use tile pattern with the same size settings as for color, set grout to black and tiles to white, bitmap for a bump is probably giving you a wider grout than tile pattern under color and this may be areason for a strang refelctions close to tiles' edges.