It just seems like an odd suggestion to me. Grout isn't expensive in and of itself. The labour to remove the grout is the most expensive part I would think.

I have a color like this on the walls of my game room, with espresso colored leather sofa and chair, and blue/teal/lime accents. I used sheers the same color as the background color on your sofa, and the room looks great. However, you could go with black, too, depending on the carpet or flooring.

I would use the greens from your bedspread. Since you have green in the bedspread, and brown and white tiles, those 3 colors need to be your focal point. So I have painted your wall a bright olive green ( the darker color in your bed spread) and the ceiling either a brown to match the tile or a white to match the rest of your ceiling. then or I think this last one is a little tamer . But you should be able to paint over the tile. WHAT kind of tile is it? If it is ceramic you can paint it. Here is a link about how to do it: https://www.sherwin-williams.com/property-facility-managers/education/styles-and-techniques/sw-article-pro-resuscitateold.html

I know all the houses in side would be beautiful, but went with the last one as the tiles outside give me enough info to have an idea of how beautiful ( if not beautiful) at least layout wise and material wise, how it would be, Now, can we see the inside please? hehe*