The very first time you saw this, were you just a bit confused, as I was?  As we all now know, the four yellow letter tiles are really white tiles.

(When Black plays a move, his move is NOT displayed with yellow letter tiles... they continue to have a black circle.)

Instead of changing the color inside the circle to indicate a move, what if the color of the cell outside the circle changed instead?  How would that look?

I think this is a big improvement.

Now all of the white letter tiles on the entire board have a white circle (with a black font).

Now all of the black letter tiles have a black circle (with a white font).

I've used a light blue color to highlight the background of the cell, to indicate the last move, but many other colors (red, green, a darker blue) look fine too.

To me, this is a better method to highlight the prior move, especially White's last move.